On the structure of the Wishart distribution
AbstractIn this paper it is shown that every nonnegative definite symmetric random matrix with independent diagonal elements and at least one nondegenerate nondiagonal element has a noninfinitely divisible distribution. Using this result it is established that every Wishart distribution Wp(k, [Sigma], M) with both p and rank ([Sigma]) >= 2 is noninfinitely divisible. The paper also establishes that any Wishart matrix having distribution Wp(k, [Sigma], 0) has the joint distribution of its elements in the rth row and rth column to be infinitely divisible for every r = 1,2,...,p.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 6 (1976)
Issue (Month): 3 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Sapatinas, Theofanis & Shanbhag, Damodar N., 2010. "Moment properties of multivariate infinitely divisible laws and criteria for multivariate self-decomposability," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 500-511, March.
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