Distributions.jl

Introduction

A Julia package for probability distributions and associated funtions. Each distribution is reified as a new type in the Julia type hierarchy deriving from the new abstract type, Distribution. These distributions minimally provide the following:

• cdf
• pdf
• quantile
• rand

Many distribution types also provide useful theoretical information about the distribution, such as:

• mean
• median
• var
• std

Supported Distributions

As of v0.0.0, the following distributions have been implemented:

• Arcsine
• Bernoulli
• Beta
• Binomial
• Categorical
• Cauchy
• Chisq
• Dirichlet
• DiscreteUniform
• Exponential
• FDist
• Gamma
• Geometric
• HyperGeometric
• InvertedGamma
• InverseWishart
• Laplace
• Logistic
• logNormal
• MixtureModel
• Multinomial
• MultivariateNormal
• NegativeBinomial
• NoncentralBeta
• NoncentralChisq
• NoncentralF
• NoncentralT
• Normal
• Pareto
• Poisson
• Rayleigh
• TDist
• Uniform
• Weibull
• Wishart

Simple Examples

using Distributions

x = rand(Normal(0.0, 1.0), 10_000)
mean(x)

d = Beta(1.0, 9.0)
pdf(d, 0.9)
quantile(d, 0.1)
cdf(d, 0.1)

Fit Distributions to Data using Maximum Likelihood Estimation

using Distributions

N = 100_000

fit(Bernoulli, rand(Bernoulli(0.7), N))

fit(Beta, rand(Beta(1.3, 3.7), N))

fit(Binomial, rand(Binomial(N, 0.3)), N)

fit(DiscreteUniform, rand(DiscreteUniform(300_000, 700_000), N))

fit(Exponential, rand(Exponential(0.1), N))

fit(Gamma, rand(Gamma(7.9, 3.1), N))

fit(Geometric, rand(Geometric(0.1), N))

fit(Laplace, rand(Laplace(10.0, 3.0), N))

fit(Normal, rand(Normal(11.3, 5.7), N))

fit(Poisson, rand(Poisson(19.0), N))

fit(Uniform, rand(Uniform(1.1, 98.3), N))