Understanding multivariate distributions

A multivariate probability distribution is one containing more than one random variable. There may or may not be any correlation among these random variables. A sample drawn from this distribution is a vector. Distributions.jl has implementations of commonly used multivariate functions—Multinomial, Multivariate Normal, and Dirichlet. They are implemented as follows:

Its type aliases are given as follows:

julia> typealias MultivariateDistribution{S<:ValueSupport} Distribution{Multivariate,S} 
 
julia> typealias DiscreteMultivariateDistribution   Distribution{Multivariate, Discrete} 
julia> typealias ContinuousMultivariateDistribution Distribution{Multivariate, Continuous} 

Most of the methods available to Univariate distributions are also available to Multivariate distributions.

Multinomial distribution

This generalizes the binomial distribution. Suppose that over a finite set of size k of a categorical distribution...