## The Annals of Mathematical Statistics

### On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix

A. W. Davis

#### 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.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 5 (1972), 1664-1670.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177692399

Digital Object Identifier
doi:10.1214/aoms/1177692399

Mathematical Reviews number (MathSciNet)
MR343465

Zentralblatt MATH identifier
0252.62028

JSTOR