Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters

Abstract

A class of ra-variate distributions with given margins and m(m -l)/2 dependence parameters, which is based on iteratively mixing conditional distributions, is derived.The family of multivariate normal distributions is a special case.The motivation for the class is to get parametric families that have m(m -l)/2 dependence parameters and properties that the family of multivariate normal distributions does not have.Properties of the class are studied, with details for (i) conditions for bivariate tail dependence and non-trivial limiting multivariate extreme value distributions and (ii) range of dependence for a bivariate measure of association such as Kendall's tau.Because tail dependence properties are one reason for studying nonmultivariate normal families, conditions for bivariate tail dependence are stud- AMS 1991

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