# 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 the Wolfram Language. 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

SplicedDistribution distribution from splicing several distributions together

### Mixtures

MixtureDistribution weighted component mixture distribution

ParameterMixtureDistribution parameter mixture distribution

CompoundPoissonDistribution compound Poisson or stopped sum 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

### Reliability »

ReliabilityDistribution reliability block diagram-based lifetime distribution

FailureDistribution fault tree-based lifetime distribution

StandbyDistribution cold, warm, etc. standby lifetime distribution

### Random Processes »

SliceDistribution distribution of one or several time slices of a random process

StationaryDistribution stationary distribution for process if it exists

### Random Graphs »

GraphPropertyDistribution distribution of properties for graphs