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Multivariate distributions and the moment problem

Lookup NU author(s): Dr Jordan Stoyanov


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For any multivariate distribution with finite moments we can ask, as in the univariate case, whether or not the distribution is uniquely determined by its moments. In this paper, we summarize, unify and extend some results that are widely scattered in the mathematical and statistical literature. We present some new results showing how to use univariate criteria together with other arguments to characterize the moment (in)determinacy of multivariate distributions. Among our examples are some classical multivariate distributions including the class of elliptically contoured distributions. Kotz-type distributions receive particular attention. We also describe some Stieltjes classes comprising distinct multivariate distributions that all possess the same set of moments. Some challenging open questions in this area are briefly outlined.

Publication metadata

Author(s): Kleiber C, Stoyanov J

Publication type: Article

Journal: Journal of Multivariate Analysis

Year: 2013

Volume: 113

Issue: 1

Pages: 7-18

Print publication date: 17/06/2011

ISSN (print): 0047-259X

ISSN (electronic): 1095-7243

Publisher: Academic Press


DOI: 10.1016/j.jmva.2011.06.001

Notes: Special Issue on Multivariate Distribution Theory in Memory of Samuel Kotz


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