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.
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Paper provided by Tecnológico de Monterrey, Campus Ciudad de México in its series EGAP Working Papers with number
200301.
Length: Date of creation: Mar 1988 Date of revision: Publication status: Published in Communications in Statistics, Theory and Methods, 1988, vol. 17,pp. 4039-4057. Handle: RePEc:ega:docume:200301
Find related papers by JEL classification: C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
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