The complex Wishart distribution and the symmetric group

• 成果类型: Article
• 署名作者: Graczyk, P; Letac, G; Massam, H
• 署名单位: Universite d'Angers; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; York University - Canada
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 287-309
• 关键词: plane partitions; moments

摘要

Let V be the space of (r, r) Hermitian matrices and let Omega be the cone of the positive definite ones. We say that the random variable S, taking its values in (Ω) over bar, has the complex Wishart distribution gamma(p,sigma) if E(exp trace(thetaS)) = (det(I-r - sigmatheta))(-p), where sigma and sigma(-1) - theta are in Omega, and where p = 1, 2,..., r - 1 or p > r - 1. In this paper, we compute all moments of S and S-1. The techniques involve in particular the use of the irreducible characters of the symmetric group.