## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Davis, A. W. On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix. Ann. Math. Statist. 43 (1972), no. 5, 1664--1670. doi:10.1214/aoms/1177692399. https://projecteuclid.org/euclid.aoms/1177692399