For Generate Random Sample, the Generalized extreme value (GEV) distribution can be defined by its mean and variance and a shape parameter (η). If η is zero the distribution is known as the Gumbel distribution, if negative as the Fréchet distribution, and if positive as the Weibull distribution. These three distributions are 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. The GEV distribution is often used as an approximation to model the maxima of long (finite) sequences of random variables.
Updated on January 30, 2023