The Exact Moments of a Ratio of Quadratic Forms in Normal Variables

Jan Magnus ()

Annals of Economics and Statistics, 1986, issue 4, 95-109

Abstract: The exact moments of x'Ax/x'Bx are obtained, where x is a normally distributed vector with some mean (possibly nonzero) and positive definite covariance matrix, A is symmetric and B positive semi definite. These moments appear as simple integrals which can be evaluated numerically in a straightforward manner. In addition, the precise conditions for the existence of the moments are found. Some related results are also reported.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:1986:i:4:p:95-109

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