Getting Started

Installation

The AdditionalDistributions package is available through the Julia package system by running Pkg.add("AdditionalDistributions"). Throughout, we assume that you have installed the package.

Starting With a Poisson Zero-infalted Distribution ZIP

We start by drawing 100 observations from a Poison zero infalted with parameters λ = 5.0 and p = 0.2 random variable.

The first step is to set up the environment:

julia> using Random, Distributions, AdditionalDistributions

julia> Random.seed!(2024) # Setting the seed

Then, we create a Poison zero infalted distribution d and obtain samples using rand:

julia> d = ZIP(5.0, 0.2)
ZIP{Float64}(λ=5.0, p=0.2)

The object d represents a probability distribution, in our case the Poison zero infalted distribution. One can query its properties such as the mean:

julia> mean(d)
4.0

We can also draw samples from d with rand.

julia> samples = rand(d, 100)
100-element Vector{Int64}:
 0
 3
 6
 4
 5
 ⋮

You can easily obtain the pdf, cdf, quantile, and many other functions for a distribution. For instance, the median (50th percentile) and the 95th percentile for the Poisson zero inflated distribution are given by:

julia> quantile.(ZIP(), [0.5, 0.95])
2-element Vector{Int64}:
 0
 2

Using Other Distributions

The package contains a large number of discrete and continuous distributions in addition to those implemented in Distributions.jl.

For instance, you can define the following distributions (among many others):

julia> BetaNegBinomial(r, α, β) # Discrete univariate
julia> Lomax(α, λ)              # Continuous univariate
julia> ZINB(r, θ, p)            # Discrete univariate
julia> Gompertz(η, b)           # Continuous univariate