On the Copula for multivariate Extreme Value distributions

TL;DR

This paper characterizes the copula structure of multivariate Extreme Value distributions, introduces the K-extremal copula with explicit density and distribution functions, and provides tools for dependence measurement, convergence analysis, and simulation.

Contribution

It establishes that all multivariate Extreme Value distributions share the same K-extremal copula and provides explicit formulas and algorithms for its analysis.

Findings

All multivariate EV distributions share the K-extremal copula.

Explicit density and distribution functions for the K-extremal copula are derived.

A simulation algorithm for the K-extremal copula is proposed.

Abstract

We show that all multivariate Extreme Value distributions, which are the possible weak limits of the $K$ largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through exact expressions for its density and distribution functions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation algorithm for the K-extremal copula.