Abstract
The marginal distributions of the latent roots of the multivariate beta matrix are shown to constitute a complete system of solutions of an ordinary differential equation (d.e.), which is related to the author's d.e.'s for Hotelling's generalized $T_0^2$ and Pillai's $V^{(m)}$ statistics. Results may be derived for the latent roots of the multivariate $F$ and Wishart matrices $(\Sigma = I)$. Pillai's approximations to the distributions of the largest and smallest roots are interpreted as exact solutions, the contributions of higher order solutions being neglected.
Citation
A. W. Davis. "On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix." Ann. Math. Statist. 43 (5) 1664 - 1670, October, 1972. https://doi.org/10.1214/aoms/1177692399
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