The Annals of Statistics

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

Marietta J. Tretter and G. William Walster

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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


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