The exact moments of a ratio of quadratic forms in normal variables
Jan R. Magnus · RePEc: Research Papers in Economics · 1986
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.