Characterization of multivariate heavy-tailed distribution families via copula

  • Authors:

  • Chengguo Weng;Yi Zhang

  • Affiliations:

  • Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310027, China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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Abstract

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies indicate that the existence of the lower tail dependence function of the survival copula is necessary and sufficient for a random vector with regularly varying univariate marginals to have a MRV tail. Moreover, the limit measure of the MRV tail is explicitly characterized. Our analysis is also extended to some more general multivariate heavy-tailed distributions, including the subexponential and the long-tailed distribution families.