Multivariate distribution models with prescribed marginals and covariances

Two multivariate distribution models consistent with prescribed marginal distributions and covariances are presented. The models are applicable to arbitrary number of random variables and are particularly suited for engineering applications. Conditions for validity of each model and applicable ranges of correlation coefficients between the variables are determined. Formulae are developed which facilitate evaluation of the model parameters in terms of the prescribed marginals and covariances. Potential uses of the two models in engineering are discussed.