In
probability theory and
statistics, the
generalized extreme value (
GEV)
distribution is a family of continuous
probability distributions developed within
extreme value theory to combine the
Gumbel,
Fréchet and
Weibull families also known as type I, II and III extreme value distributions. By the
extreme value theorem the GEV distribution is the only possible limit distribution of properly normalized maxima of a sequence of independent and identically distributed random variables. Note that a limit distribution need not exist: this requires regularity conditions on the tail of the distribution. Despite this, the GEV distribution is often used as an approximation to model the maxima of long (finite) sequences of random variables.