©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc. MARCEL DEKKER, INC. • 270 MADISON AVENUE • NEW YORK, NY 10016 DISTRIBUTIONS AND MODELS SINGULAR ELLIPTICAL DISTRIBUTION: DENSITY AND APPLICATIONS Jose´ A. Dı´az-Garcı´a, 1 Vı´ctor Leiva-Sa´nchez, 2, * and Manuel Galea 2,y 1 Department of Statistics and Computation, Universidad Auto´noma Agraria Antonio Narro, 25350 Buenavista, Saltillo, Coahuila, Me´xico E-mail: jadiaz@uaaan.mx 2 Department of Statistics, Universidad de Valparaı´so, Casilla 5030, Valparaı´so, Chile ABSTRACT The paper present an explicit expression for the density of a n-dimensional random vector with a singular Elliptical distribution. Based on this, the densities of the generalized Chi-squared and generalized t distributions are derived, examining the Pearson Type VII distribution and Kotz Type distribution (as specific Elliptical distributions). Finally, the results are applied to the study of the distribution of the residuals of an Elliptical linear model and the distribu- tion of the t-statistic, based on a sample from an Elliptical population. 665 Copyright & 2002 by Marcel Dekker, Inc. www.dekker.com COMMUN. STATIST.—THEORY METH., 31(5), 665–681 (2002) *E-mail: victor.leiva@uv.cl y E-mail: manuel.galea@uv.cl