Multivariate Distributions

It is a commonplace for all fields of computational mathematics that in the multivariate situation everything becomes much more difficult. But on the other hand tools for handling multivariate distributions are of greatest importance as one of the most common modeling errors is to overlook dependencies between input variables of a stochastic system. This error can make simulation results totally useless. Thus it is important to have generation procedures for random vectors available. There are few commonly accepted standard distributions for random vectors; even for these distributions generation procedures are difficult to find. Nevertheless, there are quite a few papers discussing the design of multivariate families that are well suited for random vector generation. For many of these families the marginals are known as well. The monograph of Johnson (1987) is presenting this branch of multivariate simulation. You can also find many of these distributions in Devroye (1986a, Chap. XI).