Multivariate Extreme Value Theory

Abstract

Abstract We consider multivariate extreme value theory as motivated by the appropriate limit laws, leading to the characterizations by the domain of attraction. We then consider characterizations of the form of the cumulative distribution function G in the bivariate case: bivariate extreme value distributions were studied extensively in the mid‐twentieth century. We focus on the developments since this pioneering work, including a range of explicit multivariate extreme models, their estimation and simulation. Moving away from pure multivariate extreme models, we consider the conditional approach for multivariate extremes, which provides a flexible range of more realistic models for use in practice. We finish with a brief review of spatial extremes, covered in detail in extremes: spatial parametric modeling.