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

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  • Khatri, C. G.

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.

Suggested Citation

  • Khatri, C. G., 1971. "Series representations of distributions of quadratic form in the normal vectors and generalised variance," Journal of Multivariate Analysis, Elsevier, vol. 1(2), pages 199-214, June.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:2:p:199-214
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    Cited by:

    1. Gao, Hongsheng & Smith, Peter J., 2000. "A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 155-165, May.

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