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Multivariate Survival Functions with a Min-Stable Property

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  • Joe, Harry
  • Ma, Chunsheng

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:75:y:2000:i:1:p:13-35
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    References listed on IDEAS

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    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    2. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    3. 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.
    4. W. R. van Zwet, 1964. "Convex transformations: A new approach to slcewness and kurtosis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 18(4), pages 433-441, December.
    5. 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.
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    Cited by:

    1. 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.
    2. 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.

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