On the structure of the Wishart distribution

D. N. Shanbhag

Journal of Multivariate Analysis, 1976, vol. 6, issue 3, 347-355

Abstract: In 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.

Keywords: Wishart; distribution; infinitely; divisible; distributions (search for similar items in EconPapers)
Date: 1976
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