Extreme value distribution

extreme value distribution

1. 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 function

   

   where 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)

   
   
2. 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.
   
   

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