An identity for the noncentral wishart distribution with application
Journal of Multivariate Analysis
Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems
IEEE Journal on Selected Areas in Communications
On the existence of non-central Wishart distributions
Journal of Multivariate Analysis
On a symbolic representation of non-central Wishart random matrices with applications
Journal of Multivariate Analysis
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While the noncentral Wishart distribution is generally introduced as the distribution of the random symmetric matrix Y"1^*Y"1+...+Y"n^*Y"n where Y"1,...,Y"n are independent Gaussian rows in R^k with the same covariance, the present paper starts from a slightly more general definition, following the extension of the chi-square distribution to the gamma distribution. We denote by @c(p,a;@s) this general noncentral Wishart distribution: the real number p is called the shape parameter, the positive definite matrix @s of order k is called the shape parameter and the semi-positive definite matrix a of order k is such that the matrix @w=@sa@s is called the noncentrality parameter. This paper considers three problems: the derivation of an explicit formula for the expectation of tr(Xh"1)...tr(Xh"m) when X~@c(p,a,@s) and h"1,...,h"m are arbitrary symmetric matrices of order k, the estimation of the parameters (a,@s) by a method different from that of Alam and Mitra [K. Alam, A. Mitra, On estimated the scale and noncentrality matrices of a Wishart distribution, Sankhya, Series B 52 (1990) 133-143] and the determination of the set of acceptable p's as already done by Gindikin and Shanbag for the ordinary Wishart distribution @c(p,0,@s).