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On the extremal dependence coefficient of multivariate distributions

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  • Frahm, Gabriel

Abstract

A measure called 'extremal dependence coefficient' (EDC) is introduced for studying the asymptotic dependence structure of the minimum and the maximum of a random vector. Some general properties of the EDC are derived and its relation to the tail dependence coefficient is examined. The extremal dependence structure of regularly varying elliptical random vectors is investigated and it is shown that the EDC is only determined by the tail index and by the pseudo-correlation coefficients of the elliptical distribution.

Suggested Citation

  • Frahm, Gabriel, 2006. "On the extremal dependence coefficient of multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1470-1481, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1470-1481
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    References listed on IDEAS

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    1. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    2. Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 275-286, July.
    3. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
    4. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

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    2. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    3. Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    4. Banachewicz, Konrad & van der Vaart, Aad, 2008. "Tail dependence of skewed grouped t-distributions," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2388-2399, October.
    5. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    6. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    7. Xie, Jiehua & Lin, Feng & Yang, Jingping, 2017. "On a generalization of Archimedean copula family," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 121-129.
    8. Karl Friedrich Siburg & Christopher Strothmann & Gregor Wei{ss}, 2022. "Comparing and quantifying tail dependence," Papers 2208.10319, arXiv.org.
    9. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    10. Siburg, Karl Friedrich & Strothmann, Christopher & Weiß, Gregor, 2024. "Comparing and quantifying tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 95-103.

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