Multivariate distributions from mixtures of max-infinitely divisible distributions. (English) Zbl 0863.62047

Joe, Harry; Hu, Taizhong

J. Multivariate Anal. 57, No. 2, 240-265 (1996).

Summary: 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.

MSC:

62H05	Characterization and structure theory for multivariate probability distributions; copulas
60E07	Infinitely divisible distributions; stable distributions

Keywords:

max-stable; multivariate extreme value distribution; copula; positive dependence; Laplace transform; survival function; mixtures; powers of a max-infinitely divisible distribution; weighted minima; maxima; families of multivariate copulas; dependence structure; cumulative distribution functions; dependence properties; characterizations