The Annals of Mathematical Statistics

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

A. W. Davis

Full-text: Open access

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


Export citation