The Laplace transform (dets)−pexptr(s−1w) and the existence of non-central Wishart distributions

Gérard Letac and Hélène Massam

Journal of Multivariate Analysis, 2018, vol. 163, issue C, 96-110

Abstract: The problem considered in this paper is to find when the non-central Wishart distribution, defined on the cone Pd¯ of positive semidefinite matrices of order d and with a real-valued shape parameter p, does exist. This can be reduced to the study of the measures m(n,k,d) defined on Pd¯ and with Laplace transform (dets)−n∕2exptr(s−1w), where n is an integer and w=diag(0,…,0,1,…,1) has order d and rank k. Our two main results are the following: we compute m(d−1,d,d) and we show that neither m(d−2,d,d) nor m(d−2,d−1,d) exists. These facts solve the problems of the existence and computation of these non-central Wishart distributions.

Keywords: Euclidean Jordan algebras; Non-central Wishart; Random matrices; Zonal polynomials (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2017.10.005

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