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On the Noncentral Distributions of the Second Largest Roots of Three Matrices in Multivariate Analysis

Published online by Cambridge University Press:  20 November 2018

Sabri Al-Ani
Sabri Al-Ani*
Affiliation:
University of Calgary, Calgary, Alberta
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The central distribution of the second largest (smallest) root following the Fisher-Girshick-Hsu-Roy distribution under certain null-hypothesis has been derived in series form by Pillai and Al-Ani [6]. In this paper the noncentral distributions of the second largest roots in the MANOVA situation, the canonical correlation, and equality of two covariance matrices are obtained. Further, the distribution of the second largest root of the covariance matrix is obtained as a limiting case. The largest root and its noncentral distributions have been considered already by Pillai and Sugiyama [7] for the situations stated above. However, in the present paper, the joint densities of the largest and the second largest roots are derived in all the above cases from which the distributions of the largest roots can be obtained, although in more elaborate forms.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 3 , September 1970 , pp. 299 - 304
Copyright
Copyright © Canadian Mathematical Society 1970

Footnotes

(1)

This research was supported by the NSF Grant GP 7663, and this paper was written when the author was at Purdue University.

References

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