Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions

✍ Scribed by Harry Joe; Taizhong Hu

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 717 KB
• Volume: 57
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1996.0032

✦ Synopsis

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.