Modeling multivariate extremes

Abstract

AbstractThe Central Limit Theorem justifies using a normal distribution when looking at sums of many terms. In a parallel way, extreme value distributions arise in the study of maxima of many terms. The goal of this paper is to briefly review the univariate theory of extremes based on the Fisher‐Tippet‐Gnedenko Theorem. We then state the basics of the multivariate theory, which is significantly more complicated because it requires a measure to define the distribution. Some properties of these laws are explored, including a description of the support, an expression for the density when it exists, and some examples that illustrate possible joint dependence structures.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Applications of Computational Statistics > Computational Finance