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Multivariate Survival Functions with a Min-Stable Property

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  • Joe, Harry
  • Ma, Chunsheng
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    Abstract

    This paper introduces and studies a class of multivariate survival functions with given univariate marginal G0, called min-stable multivariate G0-distributions, which includes min-stable multivariate exponential distributions as a special case. The representation of the form of Pickands (1981) is derived, and some dependence and other properties of the class are given. The functional form of the class is G0(A), where A is a homogeneous function on n+. Conditions are obtained for G0 and A so that a proper multivariate survival function obtains. Interesting special cases are studied including the case where G0 is a Gamma distribution.

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    Bibliographic Info

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

    Volume (Year): 75 (2000)
    Issue (Month): 1 (October)
    Pages: 13-35

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    Handle: RePEc:eee:jmvana:v:75:y:2000:i:1:p:13-35

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    Related research

    Keywords: min-stable; min-infinite divisibility; weighted minima; positive dependence; copula;

    References

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    1. 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.
    2. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    3. Joe, Harry & Hu, Taizhong, 1996. "Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 240-265, May.
    4. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
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    Cited by:
    1. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    2. 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.

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