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Zbl 1236.62048
Weng, Chengguo; Zhang, Yi
Characterization of multivariate heavy-tailed distribution families via copula. (English)
[J] J. Multivariate Anal. 106, 178-186 (2012). ISSN 0047-259X

Summary: 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.

MSC 2000:: *62H05 Multivariate structure theory
62G32 Statistics of extreme values; tail inference

Keywords: multivariate regular variation; tail dependence function; multivariate subexponential distributions; multivariate long-tailed distributions

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