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@@ -24,7 +24,7 @@ jobs: | |
fail-fast: false | ||
matrix: | ||
version: | ||
- '1.0' | ||
- '1.3' | ||
- '1' | ||
- 'nightly' | ||
os: | ||
|
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# Censored Distributions | ||
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In *censoring* of data, values exceeding an upper limit (right censoring) or falling below a lower limit (left censoring), or both (interval censoring) are replaced by the corresponding limit itself. | ||
The package provides the `censored` function, which creates the most appropriate distribution to represent a censored version of a given distribution. | ||
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A censored distribution can be constructed using the following signature: | ||
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```@docs | ||
censored | ||
``` | ||
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In the general case, this will create a `Distributions.Censored{typeof(d0)}` structure, defined as follows: | ||
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```@docs | ||
Distributions.Censored | ||
``` | ||
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In general, `censored` should be called instead of the constructor of `Censored`, which is not exported. | ||
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Many functions, including those for the evaluation of pdf and sampling, are defined for all censored univariate distributions: | ||
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- [`maximum(::UnivariateDistribution)`](@ref) | ||
- [`minimum(::UnivariateDistribution)`](@ref) | ||
- [`insupport(::UnivariateDistribution, x::Any)`](@ref) | ||
- [`pdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`logpdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`cdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`logcdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`logdiffcdf(::UnivariateDistribution, ::T, ::T) where {T <: Real}`](@ref) | ||
- [`ccdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`logccdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`quantile(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`cquantile(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`invlogcdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`invlogccdf(::UnivariateDistribution, ::Real)`](@ref) | ||
- [`median(::UnivariateDistribution)`](@ref) | ||
- [`rand(::UnivariateDistribution)`](@ref) | ||
- [`rand!(::UnivariateDistribution, ::AbstractArray)`](@ref) | ||
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Some functions to compute statistics are available for the censored distribution if they are also available for its truncation: | ||
- [`mean(::UnivariateDistribution)`](@ref) | ||
- [`var(::UnivariateDistribution)`](@ref) | ||
- [`std(::UnivariateDistribution)`](@ref) | ||
- [`entropy(::UnivariateDistribution)`](@ref) | ||
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For example, these functions are available for the following uncensored distributions: | ||
- `DiscreteUniform` | ||
- `Exponential` | ||
- `LogUniform` | ||
- `Normal` | ||
- `Uniform` | ||
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[`mode`](@ref) is not implemented for censored distributions. |
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# Convolutions | ||
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A [convolution of two probability distributions](https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions) | ||
is the probability distribution of the sum of two independent random variables that are | ||
distributed according to these distributions. | ||
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The convolution of two distributions can be constructed with [`convolve`](@ref). | ||
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```@docs | ||
convolve | ||
``` |
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