AdditionalDistributions.jl

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AdditionalDistributions.jlAdditional probability distributions for Julia

Continuous, discrete, and multivariate distributions with a familiar Distributions.jl interface.

Getting started
Distribution index
Multivariate CDFs
Benchmarks
AdditionalDistributions.jl

AdditionalDistributions.jl ​

AdditionalDistributions.jl extends the Julia statistics ecosystem with additional probability distributions while following the Distributions.jl interface whenever possible.

Main features ​

  • Continuous and discrete probability distributions beyond the core Distributions.jl catalog.

  • Zero-inflated, heavy-tailed, reliability, and count models.

  • Multivariate Gaussian and Student-t distributions.

  • Rectangular multivariate CDF evaluation through randomized QMC.

  • Direct cdf_result interoperability with native MvNormal and MvTDist.

  • Reproducible numerical integration and structured diagnostics.

  • Examples with packages from the Julia statistics ecosystem.

Installation ​

julia
using Pkg
Pkg.add("AdditionalDistributions")

Quick example ​

julia
using AdditionalDistributions
using Distributions

d = Lomax(2.0, 3.0)

pdf(d, 1.5)
cdf(d, 1.5)
quantile(d, 0.9)

Browse the Distribution index for the available distributions.

Multivariate probabilities ​

For a multivariate random vector (X), rectangular probabilities have the form

julia
using AdditionalDistributions
using LinearAlgebra
using Random

d = 5
Σ = fill(0.5, d, d)
Σ[diagind(Σ)] .= 1.0

lower = fill(-1.0, d)
upper = fill(1.0, d)

dist = MvGaussian(zeros(d), Σ)
res = cdf_result(dist, lower, upper; m=100_000, rng=MersenneTwister(1234))

res.value
res.error
res.inform

The same cdf_result interface is available for native Distributions.MvNormal and Distributions.MvTDist objects.

Numerical validation ​

The multivariate numerical core is validated with deterministic structured reference probabilities whenever available.

Independent comparisons with MvNormalCDF.jl, SciPy, and R's mvtnorm are used to evaluate accuracy and performance, but randomized external implementations are not treated as ground truth.

See Accuracy, Benchmarks, and Multivariate distributions for details.

Explore ​