Series representations of distributions of quadratic form in the normal vectors and generalised variance

C. G. Khatri

Journal of Multivariate Analysis, 1971, vol. 1, issue 2, 199-214

Abstract: Let the column vectors of X: p - n be distributed as independent normals with the same covariance matrix [Sigma]. Then, the quadratic form in normal vectors is denoted by XAX' = S, where A: n - n is a symmetric matrix which is assumed to be positive definite. This paper deals with the various series representations of the density function of S when E(X) = 0, extending the idea of Kotz et al. (1967) to the multivariate case. Further, it gives the distribution of S when E(X) [not equal to] 0, and the results for the univariate distribution of the quadratic form in noncentral normal variates can be obtained by putting p = 1.

Keywords: Distributions; quadratic; forms; series; representation; generalized; variance (search for similar items in EconPapers)
Date: 1971
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