  The problem of determining the joint probability distributions for correlated
random variables with pre-specified marginals is considered. When the joint
distribution satisfying all the required conditions is not unique, the "most
unbiased" choice corresponds to the distribution of maximum entropy. The
calculation of the maximum entropy distribution requires the solution of rather
complicated nonlinear coupled integral equations, exact solutions to which are
obtained for the case of Gaussian marginals; otherwise, the solution can be
expressed as a perturbation around the product of the marginals if the marginal
moments exist.
