## The Annals of Statistics

- Ann. Statist.
- Volume 3, Number 2 (1975), 467-472.

### Central and Noncentral Distributions of Wilks' Statistic in Manova as Mixtures of Incomplete Beta Functions

Marietta J. Tretter and G. William Walster

#### Abstract

In this paper it is shown that the distribution of the product of independently distributed beta random variables can be represented as a mixture of beta distributions. This result is then applied to derive the distributions of Wilks' statistic in the central and the noncentral linear cases. In the noncentral linear case the results of computations agree with those of Gupta (1971).

#### Article information

**Source**

Ann. Statist., Volume 3, Number 2 (1975), 467-472.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343073

**Digital Object Identifier**

doi:10.1214/aos/1176343073

**Mathematical Reviews number (MathSciNet)**

MR368312

**Zentralblatt MATH identifier**

0305.62033

**JSTOR**

links.jstor.org

**Keywords**

Statistics Distribution Theory Multivariate Analysis Analysis of Variance Incomplete beta function mixtures Wilks' likelihood ratio criterion Wilks' LRC distributions multivariate analysis of variance

#### Citation

Tretter, Marietta J.; Walster, G. William. Central and Noncentral Distributions of Wilks' Statistic in Manova as Mixtures of Incomplete Beta Functions. Ann. Statist. 3 (1975), no. 2, 467--472. doi:10.1214/aos/1176343073. https://projecteuclid.org/euclid.aos/1176343073