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EXPRESSIONS FOR INVERSE MOMENTS OF POSITIVE QUADRATIC FORMS IN NORMAL VARIABLES
Authors:M. C. Jones
Affiliation:University of Birmingham, UK
Abstract:A unified approach to the provision of exact expressions for inverse moments of positive quadratic forms in normal variables is described, using the method of (essentially) integrating the moment-generating-function (Cressie, Davis, Folks & Policello (1981). A number of special cases, many familiar from the literature, are reviewed; some allow closed form representations, others are expressed in terms of well-known mathematical functions. In the general case, our approach affords representations suitable for numerical computations.
Keywords:Negative moments    Weighted sums of chi-squares    Non-centrality    Moment-generating-function    Integral representations
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