Families of Multivariate Distributions

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Abstract
For many years there has been an interest in families of bivariate distributions with marginals as parameters. Genest and MacKay (1986a,b) showed that several such families that appear in the literature can be derived by a unified method. A similar conclusion is obtained in this article through the use of mixture models. These models might be regarded as multivariate proportional hazards models with random constants of proportionality. The mixture models are useful for two purposes. First, they make some properties of the derived distributions more transparent; the positive-dependency property of association is sometimes exposed, and a method for simulation of data from the distributions is suggested. But the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters, and they indicate obvious multivariate extensions. Some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter ...

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