Wishart and pseudo-Wishart distributions and some applications to shape theory
Journal of Multivariate Analysis
Singular random matrix decompositions: distributions
Journal of Multivariate Analysis
Complex singular wishart matrices and applications
Computers & Mathematics with Applications
Quadratic forms on complex random matrices and multiple-antenna systems
IEEE Transactions on Information Theory
Exact nonnull distribution of Wilks' statistic: The ratio and product of independent components
Journal of Multivariate Analysis
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In this paper, we determine the symmetrised density of doubly noncentral singular matrix variate beta type I and II distributions under different definitions. As particular cases we obtain the noncentral singular matrix variate beta type I and II distributions and the corresponding joint density of the nonnull eigenvalues. In addition, we propose an alternative approach to find the corresponding nonsymmetrised densities. From the latter, we solve the integral proposed by Constantine [Noncentral distribution problems in multivariate analysis, Ann. Math. Statist. 34 (1963) 1270-1285] and Khatri [A note on Mitra's paper ''A density free approach to the matrix variate beta distribution'', Sankhya A 32 (1970) 311-318] and reconsidered in Farrell [Multivariate Calculation: Use of the Continuous Groups, Springer Series in Statistics, Springer, New York, 1985, p. 191], see also Diaz-Garcia and Gutierrez-Jaimez [Noncentral matrix variate beta distribution, Comunicacion Tecnica, No. I-06-06 (PE/CIMAT), Guanajuato, Mexico, 2006, ], for the singular and nonsingular cases.