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June, 1968 On the Moment Generating Function of Pillai's $V^{(s)}$ Criterion
K. C. Sreedharan Pillai
Ann. Math. Statist. 39(3): 877-880 (June, 1968). DOI: 10.1214/aoms/1177698319


The moment generating function (mgf) of Pillai's $V^{(s)}$ criterion in the central case has been considered by Pillai [8], [9] and James [3]. In the present paper, the mgf's of $V^{(s)}$ are considered in the following non-central cases: (i) MANOVA and (ii) canonical correlation. The lower order moments of $V^{(s)}$ for (i) and (ii) in the non-central case were obtained earlier by Pillai [10] for $s = 2$ in the linear case i.e. when there is only one non-zero population root. These results for (i) were extended by Khatri and Pillai [5], [6], [7] to general $s$ in the linear case and in the planar case i.e. when there are two non-zero population roots. Only the first two moments were considered in the planar case while the first four moments were obtained in the linear case. The results of this paper further facilitates the derivation of the general moments.


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K. C. Sreedharan Pillai. "On the Moment Generating Function of Pillai's $V^{(s)}$ Criterion." Ann. Math. Statist. 39 (3) 877 - 880, June, 1968.


Published: June, 1968
First available in Project Euclid: 27 April 2007

zbMATH: 0244.62041
MathSciNet: MR230419
Digital Object Identifier: 10.1214/aoms/1177698319

Rights: Copyright © 1968 Institute of Mathematical Statistics

Vol.39 • No. 3 • June, 1968
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