Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions |
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Authors: | Harry Joe Taizhong Hu |
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Institution: | aUniversity of British Columbia, Vancouver, Canada;bUniversity of Science and Technology of China, Hefei, Anhui, People's Republic of China |
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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. |
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Keywords: | Max-stable max-infinitely divisible multivariate extreme value distribution copula positive dependence Laplace transform |
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