Distribution of the likelihood ratio criterion for testing [Sigma] = [Sigma]0, [mu] = [mu]0

Abstract

The exact null distribution of the likelihood ratio criterion for testing H0: [Sigma] = [Sigma]0 and [mu] = [mu]0 against alternatives H1: [Sigma] [not equal to] [Sigma]0 or [mu] [not equal to] [mu]0 in Np([mu], [Sigma]) has been obtained as (a) a chi-square series and (b) a beta series. Percentage points have been tabulated for p = 2(1) 6, [alpha] = .005, .01, .025, .05, .1, and .25 and various values of sample size N.Exact null distribution likelihood ratio criterion chi-square series beta series test specifying mean vector and covariance matrix percentage points