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

(RefLink[TransformedDistribution, paclet:ref/TransformedDistribution]) — distribution of a function of a random variable

(RefLink[OrderDistribution, paclet:ref/OrderDistribution]) — distribution of order statistics

(RefLink[SplicedDistribution, paclet:ref/SplicedDistribution]) — distribution from splicing several distributions together

Mixtures

(RefLink[MixtureDistribution, paclet:ref/MixtureDistribution]) — weighted component mixture distribution

(RefLink[ParameterMixtureDistribution, paclet:ref/ParameterMixtureDistribution]) — parameter mixture distribution

(RefLink[CompoundPoissonDistribution, paclet:ref/CompoundPoissonDistribution]) — compound Poisson or stopped sum distribution

Truncation and Censoring

(RefLink[TruncatedDistribution, paclet:ref/TruncatedDistribution]) — conditional distribution with variable restricted to subdomain

(RefLink[CensoredDistribution, paclet:ref/CensoredDistribution]) — distribution of censored random variables

Multivariate

(RefLink[CopulaDistribution, paclet:ref/CopulaDistribution]) — multivariate distribution from kernel and marginal distributions

(RefLink[ProductDistribution, paclet:ref/ProductDistribution]) — multivariate distribution from independent random variables

(RefLink[MarginalDistribution, paclet:ref/MarginalDistribution]) — marginal distributions in one or more variables

(OrangeLink[Reliability », paclet:guide/Reliability])

(RefLink[ReliabilityDistribution, paclet:ref/ReliabilityDistribution]) — reliability block diagram-based lifetime distribution

(RefLink[FailureDistribution, paclet:ref/FailureDistribution]) — fault tree-based lifetime distribution

(RefLink[StandbyDistribution, paclet:ref/StandbyDistribution]) — cold, warm, etc. standby lifetime distribution

(OrangeLink[Random Processes », paclet:guide/RandomProcesses])

(RefLink[SliceDistribution, paclet:ref/SliceDistribution]) — distribution of one or several time slices of a random process

(RefLink[StationaryDistribution, paclet:ref/StationaryDistribution]) — stationary distribution for process if it exists

(OrangeLink[Random Graphs », paclet:guide/RandomGraphs])

(RefLink[GraphPropertyDistribution, paclet:ref/GraphPropertyDistribution]) — distribution of properties for graphs