Extreme Value Theory (EVT) Application on Estimating the Distribution of Maxima

摘要

Extreme Value Theory (EVT) has emerged as one of the most important statistical theories for the applied sciences. EVT provides a firm theoretical foundation for building a statistical model describing extreme events. The feature that distinguish extreme value analysis than other statistical analysis is the ability to quantify the behavior of unusually large values even when those values are scarce. One of the key results from EVT is the ability to estimate the distribution of maximum value, that usually called as maxima, using the asymptotic argument. In order to build such models, the Fisher-Tippett theorem which specifies the form of the limit distribution for transformed maxima will be greatly used. Furthermore, it can be shown that there are only three families of possible limit laws for distribution of maxima, which are the Gumbel, Frechet, and Weibull distributions. These three distributions can be expressed in a single distribution function called the generalized extreme value (GEV) distribution.