Constructing Multivariate Distributions with Specific Marginal Distributions

A method is presented for constructing multivariate distributions with any specific set of univariate marginal distributions. This construction provides a rich class of distributions for modeling multivariate data as well as a basis for easily simulating correlated observations. The joint cdf and joint density function are expressed as explicit functions of the cdf′s and density functions for the univariate marginal distributions. The inclusion of different association parameters for different subsets of variables allows for many different patterns of associations. General properties of this class of multivariate distributions are reviewed and contour plots of selected bivariate densities are presented to illustrate the variety of possible shapes. An application to multivariate survival analysis is briefly considered.