Probability distributions with given multivariate marginals and given dependence structure

This paper provides a method of constructing multivariate distributions where both univariate marginals and a correlation matrix are given. An extension to multivariate marginals and a given intercorrelation matrix is also obtained. This method yields a family of distributions which are totally linear regressive and may be useful to generate exact samples for testing statistical models, to study structural models where the covariance structure is given, and to justify a statistical distance with mixed variables.