AdditionalDistributions.jl

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Compatibility ​

Compatibility with Distributions.jl ​

The AdditionalDistributions package is fully compatible with the Distributions.jl package. As an extension of Distributions.jl, AdditionalDistributions supports all the core functionalities provided by Distributions.jl, including but not limited to:

Truncated Distributions ​

Generate and work with truncated versions of existing distributions.

julia
julia> d = Alpha()
Alpha{Float64}(α=1.0, β=1.0)
julia> d_truncated = Truncated(d, 0.0, 1.0)
Truncated(Alpha{Float64}(α=1.0, β=1.0); lower=0.0, upper=1.0)

Censored Distributions ​

Handle censored data and perform analyses accordingly.

julia
julia> d1 = Gompertz()
Gompertz{Float64}(η=1.0, b=1.0)
d_censored = censored(d1, 1.5, 10)
Censored(Gompertz{Float64}(η=1.0, b=1.0); lower=1.5, upper=10.0)

Mixture Distributions ​

Create and analyze mixtures of different probability distributions.

julia
julia> d_mixture = MixtureModel(Maxwell, [2.0, 1.0, 5.5], [0.2, 0.5, 0.3])
MixtureModel{Maxwell}(K = 3)
components[1] (prior = 0.2000): Maxwell{Float64}(a=2.0)
components[2] (prior = 0.5000): Maxwell{Float64}(a=1.0)
components[3] (prior = 0.3000): Maxwell{Float64}(a=5.5)

Order Statistics ​

Compute and work with order statistics.

julia
julia> OrderStatistic(Burr(), 10, 1)
OrderStatistic{Burr{Float64}, Continuous}(
dist: Burr{Float64}(c=1.0, k=1.0, λ=1.0)
n: 10
rank: 1
)

julia> OrderStatistic(Logarithmic(), 10, 5)
OrderStatistic{Logarithmic{Float64}, Discrete}
(dist: Logarithmic{Float64}(a=0.5) 
n: 10 
rank: 5
)

Integration with Other Packages ​

Because of its compatibility with Distributions.jl, AdditionalDistributions seamlessly integrates with other Julia packages that also build on Distributions.jl. This includes:

  • Turing.jl: For probabilistic programming and Bayesian inference.

  • HypothesisTests.jl: For hypothesis testing and statistical testing.

  • Copulas.jl: For copula-based modeling and simulations.

This broad compatibility ensures that you can use AdditionalDistributions in a wide range of statistical applications, from advanced simulations to Bayesian analysis and hypothesis testing.