SINGULAR ELLIPTICAL DISTRIBUTION: DENSITY AND APPLICATIONS

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 distribution of the t-statistic, based on a sample from an Elliptical population.

Keywords:

• Elliptical distributions
• Singular distribution
• Generalized non-central Chi-squared and t distributions
• Elliptical linear model
• Confidence intervals
• The t-statistic

ACKNOWLEDGMENTS

This work was supported partially by Research Project DIPUV 33-2000 of the Universidad de Valparaíso-Chile, and the Research Project FONDECYT 1000424, Chile. The authors are especially grateful to the Universidad de Valparaíso, Chile, for their support. The authors also wish to express their gratitude to the referee for their helpful comments.