Extreme value distribution

From Glossary of Meteorology

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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