Multivariate distributions with given multivariate marginals and given dependence structure

Abstract

This paper provides a method of constructing multivariate distributions where both univariate margináis and correlation matrix are given. An extensión to multivariate margináis and given intercorrelation matrix is also obtained. This method yields a family of distributions which are totally linear regression and may be useful to generate exact samples for testing multivariate models, as well as for testing structural models where covariance structure is given, but the distribution need not be multivariate normal.