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Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions

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  • Joe, Harry
  • Hu, Taizhong
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    Abstract

    A class of multivariate distributions that are mixtures of the positive powers of a max-infinitely divisible distribution are studied. A subclass has the property that all weighted minima or maxima belong to a given location or scale family. By choosing appropriate parametric families for the mixing distribution and the distribution being mixed, families of multivariate copulas with a flexible dependence structure and with closed form cumulative distribution functions are obtained. Some dependence properties of the class, as well as some characterizations, are given. Conditions for max-infinite divisibility of multivariate distributions are obtained.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 57 (1996)
    Issue (Month): 2 (May)
    Pages: 240-265

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    Handle: RePEc:eee:jmvana:v:57:y:1996:i:2:p:240-265

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    Related research

    Keywords: Max-stable max-infinitely divisible multivariate extreme value distribution copula positive dependence Laplace transform;

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    Cited by:
    1. Eric Bouy?, 2001. "Multivariate Extremes at Work for Portfolio Risk Measurement," Working Papers wp01-02, Warwick Business School, Finance Group.
    2. Szego, Giorgio, 2002. "Measures of risk," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1253-1272, July.
    3. Paul Janssen & Luc Duchateau, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(2), pages 271-275, August.
    4. Szego, Giorgio, 2005. "Measures of risk," European Journal of Operational Research, Elsevier, vol. 163(1), pages 5-19, May.
    5. Joe, Harry & Ma, Chunsheng, 2000. "Multivariate Survival Functions with a Min-Stable Property," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 13-35, October.
    6. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    7. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
    8. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    9. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    10. Shi, Peng & Valdez, Emiliano A., 2014. "Multivariate negative binomial models for insurance claim counts," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 18-29.
    11. Hua, Lei & Joe, Harry, 2012. "Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 492-503.
    12. Meinel, Nina, 2007. "Untersuchung asymptotischer Eigenschaften von Schätzern diskreter bivariater Copula Modelle mit Kovariablen," Discussion Papers 82/2007, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    13. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    14. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.

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