Distribution of the likelihood ratio criterion for testing Σ = Σ0, μ = μ0

AbstractThe exact null distribution of the likelihood ratio criterion for testing H0: Σ = Σ0 and μ = μ0 against alternatives H1: Σ ≠ Σ0 or μ ≠ μ0 in Np(μ, Σ) has been obtained as (a) a chi-square series and (b) a beta series. Percentage points have been tabulated for p = 2(1) 6, α = .005, .01, .025, .05, .1, and .25 and various values of sample size N

On the distributions of a class of statistics in multivariate analysis

AbstractThe noncentral distributions of Y = Πi=1p θia(1 − θi)b are obtained, where a and b are known real numbers and θi's stand for latent roots of a matrix arising in each of three situations in multivariate normal theory, namely, test of equality of two covariance matrices, MANOVA, and canonical correlation. The study is extended to the complex case as well. The distributions are derived in terms of H-functions as a result of inverse Mellin transforms. Further, asymptotic expansions of the distribution of Y have been obtained in the case of two covariance matrices for selected values of (a, b)