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An Alternative Proof for a known Result of Noncentral Wishart Distribution

Published online by Cambridge University Press:  27 July 2009

Tian-Shyug Lee  and
Kwang-Chow Chang
Tian-Shyug Lee
Affiliation:
Department of Business Administration, College of Management, Fu-Jen Catholic University, Taipei. Taiwan, ROC
Kwang-Chow Chang
Affiliation:
Department of Statistics, College of Management, Fu-Jen Catholic University, Taipei, Taiwan, ROC
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Abstract

In the theory of multivariate statistics, it is well known that given a sample of n independent p-variate normally distributed random vectors with a common variance-covariance matrix, if at least one of the n vectors has nonzero means, then the sum of squares about the sample mean of the n vectors has a noncentral Wishart distribution. However, a detailed proof for this known result is rarely found in literature. In this paper, we present a formal and complete proof for the well-known result together with an example of its applications.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 523 - 529
Copyright
Copyright © Cambridge University Press 1997

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