# Extreme value distribution

From AMS Glossary

## extreme value distribution

- A probability distribution for a random variable obtained from another random variable
*x*, where each sample value for the derived distribution is obtained by selecting the maximum amplitude from a sequence of random values of*x*.

The most common extreme value distribution is the Gumbel distribution, defined by the cumulative probability functionwhere*x*is assumed to be exponentially distributed with mean and standard deviation equal to λ and where is equal to the sample size*N*. The double exponential form is valid when*N*is large. (Keeping 1962)

- A probability distribution indicating the probability that a measured quantity will exceed a prescribed value during the course of a given period (say, one year); used in the design of offshore and coastal structures.

In common parlance, the "100-year wave" is the wave height that has a probability of 0.01 of being exceeded within a 12-month period.*See*design wave, extreme wave height.

Keeping, E. S. 1962. Introduction to Statistical Inference. 206–207.