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Characterization of multivariate heavy-tailed distribution families via copula

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  • Weng, Chengguo
  • Zhang, Yi

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.

Suggested Citation

  • Weng, Chengguo & Zhang, Yi, 2012. "Characterization of multivariate heavy-tailed distribution families via copula," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 178-186.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:178-186
    DOI: 10.1016/j.jmva.2011.12.001
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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
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    3. Charpentier, Arthur & Segers, Johan, 2009. "Tails of multivariate Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1521-1537, August.
    4. Dominik Kortschak & Hansjörg Albrecher, 2009. "Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 279-306, September.
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    Cited by:

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    2. Di Bernardino, E. & Fernández-Ponce, J.M. & Palacios-Rodríguez, F. & Rodríguez-Griñolo, M.R., 2015. "On multivariate extensions of the conditional Value-at-Risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 1-16.

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