MATHEMATICA GUIDE

# Extreme Value Distributions

Just as normal and stable distributions are natural limit distributions when considering linear combinations such as means of independent variables, extreme value distributions are natural limit distributions when considering min and max operations of independent variables. They naturally occur in contexts such as reliability and risk where one often needs to consider the smallest or largest extremes of some quantity.

## ReferenceReference

### Generalized Extreme Value Distributions

MaxStableDistribution generalized maximum extreme value distribution

MinStableDistribution generalized minimum extreme value distribution

### Specialized Extreme Value Distributions

GumbelDistribution type I min extreme value distribution

ExtremeValueDistribution type I max extreme value distribution

FrechetDistribution type II max extreme value distribution

WeibullDistribution type III min extreme value distribution

### Order Statistics Distributions

OrderDistribution distribution for smallest value

TransformedDistribution distribution for function of values

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