A Class of Maximum-Entropy Multivariate Distributions

Carlos Urzúa

EGAP Working Papers from Tecnológico de Monterrey, Campus Ciudad de México

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.

Keywords: maximum entropy; exponential family; stochastic catastrophe theory; method of moments (search for similar items in EconPapers)
JEL-codes: C16 (search for similar items in EconPapers)
Date: 1988-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Published in Communications in Statistics, Theory and Methods, 1988, vol. 17,pp. 4039-4057.

Downloads: (external link)
http://alejandria.ccm.itesm.mx/egap/documentos/EGAP-2003-01.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to alejandria.ccm.itesm.mx:80 (No such host is known. )

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ega:docume:200301

Access Statistics for this paper

More papers in EGAP Working Papers from Tecnológico de Monterrey, Campus Ciudad de México Contact information at EDIRC.
Bibliographic data for series maintained by Amaranta Arroyo ( this e-mail address is bad, please contact ).