Type Hierarchy

All samplers and distributions provided in this package are organized into a type hierarchy described as follows.


The root of this type hierarchy is Sampleable. The abstract type Sampleable subsumes any types of objects from which one can draw samples, which particularly includes samplers and distributions. Formally, Sampleable is defined as

abstract type Sampleable{F<:VariateForm,S<:ValueSupport} end

It has two type parameters that define the kind of samples that can be drawn therefrom.




The VariateForm subtypes defined in Distributions.jl are:

TypeA single sampleMultiple samples
Univariate == ArrayLikeVariate{0}a scalar numberA numeric array of arbitrary shape, each element being a sample
Multivariate == ArrayLikeVariate{1}a numeric vectorA matrix, each column being a sample
Matrixvariate == ArrayLikeVariate{2}a numeric matrixAn array of matrices, each element being a sample matrix


The ValueSupport sub-types defined in Distributions.jl are:

Discrete <: ValueSupport

This type represents the support of a discrete random variable.

It is countable. For instance, it can be a finite set or a countably infinite set such as the natural numbers.

See also: Continuous, ValueSupport

Continuous <: ValueSupport

This types represents the support of a continuous random variable.

It is uncountably infinite. For instance, it can be an interval on the real line.

See also: Discrete, ValueSupport

TypeDefault element typeDescriptionExamples
DiscreteIntSamples take countably many values$\{0,1,2,3\}$, $\mathbb{N}$
ContinuousFloat64Samples take uncountably many values$[0, 1]$, $\mathbb{R}$

Multiple samples are often organized into an array, depending on the variate form.

The basic functionalities that a sampleable object provides are to retrieve information about the samples it generates and to draw samples. Particularly, the following functions are provided for sampleable objects:


The length of each sample. Always returns 1 when s is univariate.


The size (i.e. shape) of each sample. Always returns () when s is univariate, and (length(s),) when s is multivariate.


The number of values contained in one sample of s. Multiple samples are often organized into an array, depending on the variate form.


The default element type of a sample. This is the type of elements of the samples generated by the rand method. However, one can provide an array of different element types to store the samples using rand!.

rand(::AbstractRNG, ::Sampleable)

Samples from the sampler and returns the result.

rand!(::AbstractRNG, ::Sampleable, ::AbstractArray)

Samples in-place from the sampler and stores the result in the provided array.


We use Distribution, a subtype of Sampleable as defined below, to capture probabilistic distributions. In addition to being sampleable, a distribution typically comes with an explicit way to combine its domain, probability density function, and many other quantities.

abstract type Distribution{F<:VariateForm,S<:ValueSupport} <: Sampleable{F,S} end

To simplify the use in practice, we introduce a series of type alias as follows:

const UnivariateDistribution{S<:ValueSupport}   = Distribution{Univariate,S}
const MultivariateDistribution{S<:ValueSupport} = Distribution{Multivariate,S}
const MatrixDistribution{S<:ValueSupport}       = Distribution{Matrixvariate,S}
const NonMatrixDistribution = Union{UnivariateDistribution, MultivariateDistribution}

const DiscreteDistribution{F<:VariateForm}   = Distribution{F,Discrete}
const ContinuousDistribution{F<:VariateForm} = Distribution{F,Continuous}

const DiscreteUnivariateDistribution     = Distribution{Univariate,    Discrete}
const ContinuousUnivariateDistribution   = Distribution{Univariate,    Continuous}
const DiscreteMultivariateDistribution   = Distribution{Multivariate,  Discrete}
const ContinuousMultivariateDistribution = Distribution{Multivariate,  Continuous}
const DiscreteMatrixDistribution         = Distribution{Matrixvariate, Discrete}
const ContinuousMatrixDistribution       = Distribution{Matrixvariate, Continuous}

All methods applicable to Sampleable also apply to Distribution. The API for distributions of different variate forms are different (refer to univariates, multivariates, and matrix for details).