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Maximum-entropy distributions of correlated variables with prespecified marginals
1Instituto de Ciencias Físicas, UNAM, Apartado Postal 48-3, Codigo Postal 62251, Cuernavaca, Morelos, Mexico.
Abstract:
The problem of determining the joint probability distributions for correlated random variables with prespecified 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.
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