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International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 4, Pages 249-255
http://dx.doi.org/10.1155/S0161171202012838

Null distribution of multiple correlation coefficient under mixture normal model

Hydar Ali1 and Daya K. Nagar2

1Department of Mathematics and Computer Science, the University of the West Indies, St. Augustine, Trinidad and Tobago
2Departamento de Matemáticas, Universidad de Antioquia, Medellín A. A. 1226, Colombia

Received 14 April 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The multiple correlation coefficient is used in a large variety of statistical tests and regression problems. In this article, we derive the null distribution of the square of the sample multiple correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1−R2 and inverse Mellin transform have been used to derive the density of R2.