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On the structure of the Wishart distribution

Author

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  • Shanbhag, D. N.

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.

Suggested Citation

  • Shanbhag, D. N., 1976. "On the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 347-355, September.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:3:p:347-355
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    Cited by:

    1. 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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