Noncentral Beta Distribution Research Articles

An Asymptotic Expansion of the Nonnull Distribution of Wilks Criterion for Testing the Multivariate Linear Hypothesis

An asymptotic expansion of the nonnull distribution of the Wilks statistic for testing the linear hypothesis in multivariate analysis of variance is obtained up to the order $N^{-2}$ where $N$ is the sample size, for the first time in terms of noncentral beta distributions. The asymptotic distributions are better than the ones available in Anderson (1958) in the null case and in Sugiura and Fujikoshi (1969) and Posten and Bergman (1964) in the nonnull case. In fact, for certain parameters the asymptotic expansion reduces to the first term and we get the exact distribution.

Test of independence between tow sets of variates

In this paper asymptotic expansions of the null as well as non-null distributions of the likelihood ratio criterion for testing independence between two sets of variates are obtained. These appear to be better than the ones available in the literature . In factin the null case for p = 1 and p = 2 , t h e expansion reduces to the exact di stribution. In the non-null case, the expansion is given i n terms of non-central beta distributions and for the case when the population canonical correlation coefficients are small.

The non-central chi-squared and beta distributions

The non-central chi-squared and beta distributions

On the Noncentral Beta-Distribution

A computing formula for the noncentral beta-distribution recently published by Nicholson is simplified. A table of figurate numbers is provided to facilitate the use of the simplified formula. It is compared for ease of use with the method of Tang in several situations.