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Expansions for bivariate extreme value distributions

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  • Nadarajah, Saralees

Abstract

Expressions for moment properties have not been known even for the simplest of the bivariate extreme value distributions. Here, simple expansions are derived for various properties of any given bivariate extreme value distribution. Each expansion is a single infinite sum. The properties considered include product moments, conditional moments, joint moment generating function and others. Computational efficiencies of these expansions are established with respect to standard approaches for computing moment properties.

Suggested Citation

  • Nadarajah, Saralees, 2013. "Expansions for bivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 744-752.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:744-752
    DOI: 10.1016/j.spl.2012.11.011
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
    2. Enkelejd Hashorva, 2008. "A new family of bivariate max-infinitely divisible distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 289-304, November.
    3. Nadarajah, S., 1999. "A polynomial model for bivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 15-25, March.
    4. Hashorva, Enkelejd, 2006. "A novel class of bivariate max-stable distributions," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1047-1055, May.
    5. Cooley, Daniel & Davis, Richard A. & Naveau, Philippe, 2010. "The pairwise beta distribution: A flexible parametric multivariate model for extremes," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2103-2117, October.
    6. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.
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