On the copula for multivariate extreme value distributions

Abstract

We show that all multivariate extreme value distributions, which are the possible weak limits of the K largest order statistics of i.i.d. samples, have the same copula, the so called K-extremal copula. This copula and its density are described through exact expressions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation algorithm for the K-extremal copula.