diff --git a/src/univariate/continuous/beta.jl b/src/univariate/continuous/beta.jl index 6259b18cd2..5bc3f2f2b6 100644 --- a/src/univariate/continuous/beta.jl +++ b/src/univariate/continuous/beta.jl @@ -1,5 +1,5 @@ """ - Beta(α,β) + Beta(α, β) The *Beta distribution* has probability density function @@ -15,10 +15,10 @@ independently, then ``X / (X + Y) \\sim \\operatorname{Beta}(\\alpha, \\beta)``. ```julia Beta() # equivalent to Beta(1, 1) -Beta(a) # equivalent to Beta(a, a) -Beta(a, b) # Beta distribution with shape parameters a and b +Beta(α) # equivalent to Beta(α, α) +Beta(α, β) # Beta distribution with shape parameters α and β -params(d) # Get the parameters, i.e. (a, b) +params(d) # Get the parameters, i.e. (α, β) ``` External links diff --git a/src/univariate/continuous/betaprime.jl b/src/univariate/continuous/betaprime.jl index e965cf6741..7c30bd7ed4 100644 --- a/src/univariate/continuous/betaprime.jl +++ b/src/univariate/continuous/betaprime.jl @@ -1,5 +1,5 @@ """ - BetaPrime(α,β) + BetaPrime(α, β) The *Beta prime distribution* has probability density function @@ -15,10 +15,10 @@ relation ship that if ``X \\sim \\operatorname{Beta}(\\alpha, \\beta)`` then ``\ ```julia BetaPrime() # equivalent to BetaPrime(1, 1) -BetaPrime(a) # equivalent to BetaPrime(a, a) -BetaPrime(a, b) # Beta prime distribution with shape parameters a and b +BetaPrime(α) # equivalent to BetaPrime(α, α) +BetaPrime(α, β) # Beta prime distribution with shape parameters α and β -params(d) # Get the parameters, i.e. (a, b) +params(d) # Get the parameters, i.e. (α, β) ``` External links diff --git a/src/univariate/continuous/cauchy.jl b/src/univariate/continuous/cauchy.jl index d7a1873429..5afe79d90e 100644 --- a/src/univariate/continuous/cauchy.jl +++ b/src/univariate/continuous/cauchy.jl @@ -9,12 +9,12 @@ f(x; \\mu, \\sigma) = \\frac{1}{\\pi \\sigma \\left(1 + \\left(\\frac{x - \\mu}{ ```julia Cauchy() # Standard Cauchy distribution, i.e. Cauchy(0, 1) -Cauchy(u) # Cauchy distribution with location u and unit scale, i.e. Cauchy(u, 1) -Cauchy(u, b) # Cauchy distribution with location u and scale b +Cauchy(μ) # Cauchy distribution with location μ and unit scale, i.e. Cauchy(μ, 1) +Cauchy(μ, σ) # Cauchy distribution with location μ and scale σ -params(d) # Get the parameters, i.e. (u, b) -location(d) # Get the location parameter, i.e. u -scale(d) # Get the scale parameter, i.e. b +params(d) # Get the parameters, i.e. (μ, σ) +location(d) # Get the location parameter, i.e. μ +scale(d) # Get the scale parameter, i.e. σ ``` External links diff --git a/src/univariate/continuous/chernoff.jl b/src/univariate/continuous/chernoff.jl index 340f68b229..920f05b2c1 100644 --- a/src/univariate/continuous/chernoff.jl +++ b/src/univariate/continuous/chernoff.jl @@ -16,7 +16,7 @@ The *Chernoff distribution* is the distribution of the random variable ```math \\underset{t \\in (-\\infty,\\infty)}{\\arg\\max} ( G(t) - t^2 ), ``` -where ``G`` is standard two--sided Brownian motion. +where ``G`` is standard two-sided Brownian motion. The distribution arises as the limit distribution of various cube-root-n consistent estimators, including the isotonic regression estimator of Brunk, the isotonic density estimator of Grenander, @@ -27,21 +27,7 @@ computation of pdf and cdf is based on the algorithm described in Groeneboom and Journal of Computational and Graphical Statistics, 2001. ```julia -Chernoff() -pdf(Chernoff(),x::Real) -cdf(Chernoff(),x::Real) -logpdf(Chernoff(),x::Real) -survivor(Chernoff(),x::Real) -mean(Chernoff()) -var(Chernoff()) -skewness(Chernoff()) -kurtosis(Chernoff()) -kurtosis(Chernoff(), excess::Bool) -mode(Chernoff()) -entropy(Chernoff()) -rand(Chernoff()) -rand(rng, Chernoff() -cdf(Chernoff(),-x) #For tail probabilities, use this instead of 1-cdf(Chernoff(),x) +cdf(Chernoff(),-x) # For tail probabilities, use this instead of 1-cdf(Chernoff(),x) ``` """ struct Chernoff <: ContinuousUnivariateDistribution diff --git a/src/univariate/continuous/symtriangular.jl b/src/univariate/continuous/symtriangular.jl index 2f15f99f7a..77f25f68e7 100644 --- a/src/univariate/continuous/symtriangular.jl +++ b/src/univariate/continuous/symtriangular.jl @@ -1,5 +1,5 @@ """ - SymTriangularDist(μ,σ) + SymTriangularDist(μ, σ) The *Symmetric triangular distribution* with location `μ` and scale `σ` has probability density function @@ -9,8 +9,8 @@ f(x; \\mu, \\sigma) = \\frac{1}{\\sigma} \\left( 1 - \\left| \\frac{x - \\mu}{\\ ```julia SymTriangularDist() # Symmetric triangular distribution with zero location and unit scale -SymTriangularDist(u) # Symmetric triangular distribution with location μ and unit scale -SymTriangularDist(u, s) # Symmetric triangular distribution with location μ and scale σ +SymTriangularDist(μ) # Symmetric triangular distribution with location μ and unit scale +SymTriangularDist(μ, s) # Symmetric triangular distribution with location μ and scale σ params(d) # Get the parameters, i.e. (μ, σ) location(d) # Get the location parameter, i.e. μ