International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 555-562

Distribution of LRC for testing sphericity of a complex multivariate Gaussian model

D. K. Nagar,1 S. K. Jain,1 and A. K. Gupta2

1Department of Statistics, University of Rajasthan, Jaipur, Rajasthan, India
2Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, Ohio, USA

Received 13 February 1984

Copyright © 1985 D. K. Nagar et al. 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.


In this paper, exact null distribution of the likelihood ratio criterion for testing sphericity structure in a complex multivariate normal covariance matrix is obtained in computable series form. The method of inverse Mellin transform and contour integration has been used. Certain special cases are given explicitly in terms of the hypergeometric functions.