On some distribution problems in Manova and discriminant analysis

Asymptotic expansions, valid for large error degrees of freedom, are given for the multivariate noncentral F distribution and for the distribution of latent roots in MANOVA and discriminant analysis. The asymptotic results are expressed in terms of elementary functions which are easy to compute and the results of some numerical work are included. The Bartlett test of the null hypothesis that some of the noncentrality parameters in discriminant analysis are zero is also briefly discussed.