Doubly Non-central t and Distributions Obtained Under Singular and Non-singular Elliptic Distributions

Abstract

We find in this article the densities of the generalized doubly non-central t and distributions, under singularity and non-singularity of the Elliptic distribution associated. These results are applied to the Pearson Type VII and Normal distributions.

Keywords:

• Singular and non-singular elliptic distributions
• Generalized doubly non-central t and F distributions

Acknowledgments

This work was supported partially by the research project DIPUV 33-2000 of the Universidad de Valparaíso-Chile, and the Research Project UAAAN 02.03.0308.2627, of the Universidad Autónoma Agraria Antonio Narro, México. The authors also wish to express their gratitude to the referee for their helpful comments and to the editors.

Notes

This density have some minor mistakes. Specifically, integration order and the exponent of the constant π should be (m+n-1)/2 instead of (m+n)/2. These mistakes are evident from the density given in the Page 85 Line 3 in that same reference.