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Maximum Entropy distributions of correlated variables with prespecified marginals


  • Hern'an Larralde


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.

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  • Hern'an Larralde, 2012. "Maximum Entropy distributions of correlated variables with prespecified marginals," Papers 1212.0440,
  • Handle: RePEc:arx:papers:1212.0440

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    1. Esmaeili, Habib & Kl├╝ppelberg, Claudia, 2010. "Parameter estimation of a bivariate compound Poisson process," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 224-233, October.
    2. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
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