Given a general multivariate linear model of full or less than full rank, we find the distributions of internally and externally studentised residuals, assuming normal and elliptical distributions.

Several distributions are studied, simultaneously in the real, complex, quaternion and octonion cases. Specifically, these are the central, nonsingular matricvariate and matrix multivariate T and beta type II distributions and the joint density of the singular values are obtained for real normed...

For a singular random matrix X, we find the Jacobians associated to the following decompositions: QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, for the cross-product matrix S=X'X we find the Jacobians of the Spectral, Cholesky's, L'DL and symmetric nonnegative...

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and polar decompositions of matrix Y are determined, for central and non-central, non-singular and...

Suppose thatX~N-m([mu], [Sigma], [Theta]). An expression for the density function is given when[Sigma][greater-or-equal, slanted]0 and/or[Theta]:[greater-or-equal, slanted]0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrixZof...

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...

This paper explains the differences between the densities and the Jacobians of the transforms of the same singular random matrices treated by several authors. Some comments on the results proposed by Srivastava [Singular Wishart and multivariate beta distributions, Ann. Statist. 31 (2003)...

The noncentral configuration density, derived under an elliptical model, generalizes and corrects the Gaussian configuration and some Pearson results. Partition theory is then used to obtain explicit configuration densities associated with matrix variate symmetric Kotz type distributions...