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Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions

Author

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  • Joe, Harry
  • Hu, Taizhong

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.

Suggested Citation

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