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Derived Statistical Distributions
Derived distributions are modifications to existing distributions. There is a variety of ways in which you can arrive at modified distributions, including functions of random variables, weighted mixtures of distributions, truncated or censored distributions, marginals from higher-dimensional distributions, or joining marginals to a dependency kernel, as in copulas. Derived distributions behave just like any other distribution in Mathematica. You can compute several dozen properties, including distribution functions or probabilities of events, or generate random variates from them.
Functions of Random Variables
TransformedDistribution distribution of a function of a random variable
OrderDistribution distribution of order statistics
Mixtures
MixtureDistribution weighted component mixture distribution
ParameterMixtureDistribution parameter mixture distribution
Truncation and Censoring
TruncatedDistribution conditional distribution with variable restricted to subdomain
CensoredDistribution distribution of censored random variables
Multivariate
CopulaDistribution multivariate distribution from kernel and marginal distributions
ProductDistribution multivariate distribution from independent random variables
MarginalDistribution marginal distributions in one or more variables