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Keywords:

  • multivariate extreme value distributions;
  • extreme value copulas;
  • Marshall--Olkin models;
  • random variates generation;
  • multivariate return periods

Abstract

Copulas represent a fundamental tool for constructing multivariate probability distributions. Exploiting recent theoretical developments concerning the construction of copulas, we outline several methods for generating multivariate extreme value (MEV) laws having a suitable number of parameters, a feature of great importance in applications. The corresponding random vectors can be efficiently simulated, and easily fitted to empirical data. The use of multivariate return periods for extreme events is also discussed. A practical illustration involving maxima sampled via a network of non-independent gauge stations is presented. Copyright © 2009 John Wiley & Sons, Ltd.