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August, 1971 Noncentral Distribution of Wilks' Statistic in Manova
A. K. Gupta
Ann. Math. Statist. 42(4): 1254-1261 (August, 1971). DOI: 10.1214/aoms/1177693238


In this paper, the exact distribution of Wilks' likelihood ratio criterion, $\Lambda$, for MANOVA in the noncentral linear case i.e. when the alternative hypothesis is of unit rank, has been obtained and explicit expressions for the same for $p = 2, 3, 4$ and 5, where $p$ is the number of variables and for general $f_1$ and $f_2$ are given. A general form of the distribution of $\Lambda$ in this case, for any $p$, is also given. It has been shown that the total integral of the series obtained by taking a few terms only, rapidly approaches the theoretical value one as more terms are taken into account. Further the accuracy of the approximation, suggested by Posten and Bargmann [11], is examined numerically and it has been shown that the approximation is excellent except when $f_1$ and $f_2$ are both small and the noncentrality parameter $\lambda^2$ is large.


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A. K. Gupta. "Noncentral Distribution of Wilks' Statistic in Manova." Ann. Math. Statist. 42 (4) 1254 - 1261, August, 1971.


Published: August, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0223.62064
MathSciNet: MR292226
Digital Object Identifier: 10.1214/aoms/1177693238

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 4 • August, 1971
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