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A Class of Maximum-Entropy Multivariate Distributions

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  • Urzúa, Carlos M.

Abstract

This paper characterizes a class of multivariate distributions that includes the multinormal and is contained in the exponential family. The wide range of possible applications of these distributions is suggested by some of the characteristics germane to them: First, they maximize Shannon's entropy among all distributions that have finite moments of given orders. As such, they constitute a class of distributions that includes the multinormal and some likely alternatives. Second, they can exhibit several modes, and, furthermore, they do so with a relatively small number of parameters (compared to mixtures of multinormals). Third, they are the stationary distributions of certain diffusion processes. Fourth, they approximate, near the multinormal, the multivariate Pearson family. And fifth, the maximum likelihood estimators of their population moments are the sample moments. Two possible methods of estimating the distributions are studied in this paper: maximum likelihood estimation, and a fast procedure that can be used to find consistent estimators of the parameters via sample moments. A FORTRAN subroutine that implements the latter method is also provided.

Suggested Citation

  • Urzúa, Carlos M., 1988. "A Class of Maximum-Entropy Multivariate Distributions," EGAP Working Papers 200301, Tecnológico de Monterrey, Campus Ciudad de México.
    • Handle: RePEc:ega:docume:200301
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    File URL: http://alejandria.ccm.itesm.mx/egap/documentos/EGAP-2003-01.pdf
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    References listed on IDEAS

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    1. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
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    Cited by:

    1. Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 51-86, March.
    2. Urzúa, Carlos M., 1996. "Omnibus Tests for Multivariate Normality of Observations and Residuals," EGAP Working Papers 200304, Tecnológico de Monterrey, Campus Ciudad de México.
    3. Urzua, Carlos M., 1996. "On the correct use of omnibus tests for normality," Economics Letters, Elsevier, vol. 53(3), pages 247-251, December.

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    More about this item

    Keywords

    maximum entropy; exponential family; stochastic catastrophe theory; method of moments;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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