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June, 1954 On Multivariate Distribution Theory
I. Olkin, S. N. Roy
Ann. Math. Statist. 25(2): 329-339 (June, 1954). DOI: 10.1214/aoms/1177728789


This paper is concerned with a matrix method of deriving the sampling distributions of a large class of statistics directly from the probability law for random samples from a multivariate normal population, that is without assuming the Wishart distribution or the distribution of rectangular coordinates. Two techniques are proposed for evaluating the Jacobians of certain transformations, one based on a theorem on Jacobians [1], and the second based on the introduction of pseudo or extra variables. This matrix approach has a geometrical analog developed in part by one of the authors [2]. Section 3 is concerned with a discussion of these two techniques; in Section 4, the former is applied to obtain the joint distribution of the rectangular coordinates [3], and in Section 5, the second method is applied to obtain the joint distribution of the roots of a determinantal equation [4], [5], [6], and [7].


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I. Olkin. S. N. Roy. "On Multivariate Distribution Theory." Ann. Math. Statist. 25 (2) 329 - 339, June, 1954.


Published: June, 1954
First available in Project Euclid: 28 April 2007

zbMATH: 0055.37304
MathSciNet: MR61795
Digital Object Identifier: 10.1214/aoms/1177728789

Rights: Copyright © 1954 Institute of Mathematical Statistics

Vol.25 • No. 2 • June, 1954
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