On the cumulants of the logarithmic generalized variance and variance ratio

Summary

In dealing with certain extensions of the analysis of variance to samples from a multivariate normal population Wilks [4] introduced the quantity ‘generalized variance’ |S|, where |S| represents the determinant of the sample variances and covariances. He was able to obtain its distribution for a few special cases. The following note gives the general expressions for the cumulants of log |S| which is of interest in present asymptotic multivariate tests (cf. e.g. [2]).