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October 2003 Singular Wishart and multivariate beta distributions
M.S. Srivastava
Ann. Statist. 31(5): 1537-1560 (October 2003). DOI: 10.1214/aos/1065705118


In this article, we consider the case when the number of observations n is less than the dimension p of the random vectors which are assumed to be independent and identically distributed as normal with nonsingular covariance matrix. The central and noncentral distributions of the singular Wishart matrix $S=XX'$, where X is the $p \times n$ matrix of observations are derived with respect to Lebesgue measure. Properties of this distribution are given. When the covariance matrix is singular, pseudo singular Wishart distribution is also derived. The result is extended to any distribution of the type $f(XX')$ for the central case. Singular multivariate beta distributions with respect to Lebesgue measure are also given.


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M.S. Srivastava. "Singular Wishart and multivariate beta distributions." Ann. Statist. 31 (5) 1537 - 1560, October 2003.


Published: October 2003
First available in Project Euclid: 9 October 2003

zbMATH: 1042.62051
MathSciNet: MR2012825
Digital Object Identifier: 10.1214/aos/1065705118

Primary: 62H10
Secondary: 62E15

Keywords: Jacobian of transformations , normal distribution , pseudo Wishart , singular noncentral Wishart , Stiefel manifold

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 5 • October 2003
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