Fundamental of Extreme Value Theory

Extreme value theory deals with the stochastic behavior of the extreme values in a process. For a single process, the behavior of the maxima can be described by the three extreme value distributions–Gumbel, Fréchet and negative Weibull–as suggested by Fisher and Tippett (1928). Kotz and Nadarajah (2000) indicated that the extreme value distributions could be traced back to the work done by Bernoulli in 1709. The first application of extreme value distributions was probably made by Fuller in 1914. Thereafter, several researchers have provided useful applications of extreme value distributions particularly to climate data from different regions of the world. For a review of applications see Farago and Katz (1990).