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

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