On the Copula for multivariate Extreme Value distributions

2009/08/14 by Glauco Valle, Valle, Glauco, Marco Aurelio Sanfins +1
Mathematics · #60E99 #60G70 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60E99 #msc:60G70 #stat.TH

paper · pdf · doi:10.48550/arxiv.0908.2144

11 pages

arxiv created 2010/07/29 · arxiv updated 2015/03/13

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.

Related

• Generating multivariate extreme value distributions
• Extreme-Value Copulas
• Characterization of Extreme Copulas
• Extreme value copula estimation based on block maxima of a multivariate stationary time series
• The t Copula and Related Copulas