The exact distribution of the largest eigenvalue of a singular beta F-matrix for Roy's test

04/21/2020

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by   Koki Shimizu, et al.

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In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for Roy's test is discussed. The key to developing the distribution theory of eigenvalues of a singular random matrix is to use heterogeneous hypergeometric functions with two matrix arguments. In this study, we define the singular beta F-matrix and extend the distributions of a nonsingular beta F-matrix to the singular case. We also give the joint density function of eigenvalues and the exact distribution of the largest eigenvalue in terms of heterogeneous hypergeometric functions.