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...

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)...

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.

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...

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L´U, L´DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky´s, L´DL and symmetric non-negative...

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...

The size-and-shape and shape distributions based on non-central and non-isotropic elliptical distributions are derived in this paper by using the singular value decomposition (SVD). The general densities require the computation of new integrals involving zonal polynomials. The invariance of the...

Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then proposed. The scale mixture of left-spherical matrix variate...