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

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  • Jan R. Magnus

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.

Suggested Citation

  • Jan R. Magnus, 1986. "The Exact Moments of a Ratio of Quadratic Forms in Normal Variables," Annals of Economics and Statistics, GENES, issue 4, pages 95-109.
    • Handle: RePEc:adr:anecst:y:1986:i:4:p:95-109
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