AdditionalDistributions.jl

Appearance

Ecosystem integration ​

AdditionalDistributions.jl is designed to integrate with the Julia statistics ecosystem. Since the package follows the Distributions.jl interface whenever possible, its distributions can be used in simulation, statistical testing, copula modeling, Bayesian inference, and probabilistic programming workflows.

This page summarizes how AdditionalDistributions.jl works with packages such as Distributions.jl, HypothesisTests.jl, Copulas.jl, StatsBase.jl, and Turing.jl.

Distributions.jl ​

The package extends the usual distribution interface:

julia
pdf(d, x)
logpdf(d, x)
cdf(d, x)
quantile(d, p)
rand(rng, d)
mean(d)
var(d)

This makes the distributions usable in many packages that already depend on the Distributions.jl API.

HypothesisTests.jl ​

Samples generated from distributions in AdditionalDistributions.jl can be used directly with classical statistical tests.

For example, univariate samples can be compared with:

julia
ApproximateTwoSampleKSTest(x, y)
MannWhitneyUTest(x, y)

Multivariate samples from MvGaussian can be used with:

julia
UnequalCovHotellingT2Test(X, Y)
EqualCovHotellingT2Test(X, Y)
BartlettTest(X, Y)

See examples/scripts/06_hypothesistests.jl.

Copulas.jl ​

Marginal distributions from AdditionalDistributions.jl can be combined with copulas through SklarDist.

julia
C = GaussianCopula(Σ)

marginals = (
    Burr(1.6, 2.5, 1_000.0),
    Dagum(2.0, 1_000.0, 1.5),
)

joint = SklarDist(C, marginals)

See examples/scripts/07_copulas_sklar.jl.

Turing.jl ​

Distributions with compatible logpdf methods can be used inside Bayesian models in Turing.jl.

julia
@model function maxwell_model(x)
    σ ~ truncated(Normal(1.5, 0.5), 0.1, 5.0)

    for i in eachindex(x)
        x[i] ~ Maxwell(σ)
    end
end

See examples/scripts/08_turing_model.jl.

Notes ​

Some advanced distributions may have infinite or undefined moments depending on their parameter values. This is expected for heavy-tailed models and should be considered when using empirical summaries, hypothesis tests, or Bayesian models.