MULTIVARIATE DISTRIBUTIONS FROM MIXTURES OF MAX-INFINITELY DIVISIBLE DISTRIBUTIONS

A class of multivariate distributions that are mixtures of the positiv e powers of a max-infinitely divisible distribution are studied. A sub class has the property that all weighted minima or maxima belong to a given location or scale family. By choosing appropriate parametric fam ilies for the mixing distribution and the distribution being mixed, fa milies of multivariate copulas with a flexible dependence structure an d with closed form cumulative distribution functions are obtained. Som e dependence properties of the class, as well as some characterization s, are given. Conditions for max-infinite divisibility of multivariate distributions are obtained. (C) 1996 Academic Press, Inc.