truncate.md

Truncated Distributions

The package provides the truncated function which creates the most appropriate distribution to represent a truncated version of a given distribution.

A truncated distribution can be constructed using the following signature:

truncated

In the general case, this will create a Truncated{typeof(d)} structure, defined as follows:

Truncated

Many functions, including those for the evaluation of pdf and sampling, are defined for all truncated univariate distributions:

• maximum(::UnivariateDistribution)
• minimum(::UnivariateDistribution)
• insupport(::UnivariateDistribution, x::Any)
• pdf(::UnivariateDistribution, ::Real)
• logpdf(::UnivariateDistribution, ::Real)
• gradlogpdf(::UnivariateDistribution, ::Real)
• cdf(::UnivariateDistribution, ::Real)
• logcdf(::UnivariateDistribution, ::Real)
• logdiffcdf(::UnivariateDistribution, ::T, ::T) where {T <: Real}
• ccdf(::UnivariateDistribution, ::Real)
• logccdf(::UnivariateDistribution, ::Real)
• quantile(::UnivariateDistribution, ::Real)
• cquantile(::UnivariateDistribution, ::Real)
• invlogcdf(::UnivariateDistribution, ::Real)
• invlogccdf(::UnivariateDistribution, ::Real)
• rand(::UnivariateDistribution)
• rand!(::UnivariateDistribution, ::AbstractArray)
• median(::UnivariateDistribution)

Functions to compute statistics, such as mean, mode, var, std, and entropy, are not available for generic truncated distributions. Generally, there are no easy ways to compute such quantities due to the complications incurred by truncation. However, these methods are supported for truncated normal distributions Truncated{<:Normal} which can be constructed with truncated(::Normal, ...).