Nonnull distributions of some statistics associated with testing for the equality of two covariance matrices

Abstract

The nonnull distribution of some statistics, used for testing [Sigma]1 = [Sigma]2 are obtained as mixtures of incomplete beta functions as well as mixtures of incomplete gamma functions. The introduction of the convergence factors and certain recurrence relations are useful in the computation of the power of the tests as well as computation of exact percentage points for tests of significance.Nonnull distributions hypergeometric functions of matrix argument zonal polynomial mixtures of beta functions and gamma functions