TY - JOUR
T1 - Singular elliptical distribution
T2 - Density and applications
AU - Díaz-García, José A.
AU - Leiva-Sánchez, Victor
AU - Galea, Manuel
N1 - Funding Information:
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.
PY - 2002/5
Y1 - 2002/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=31244433378&partnerID=8YFLogxK
U2 - 10.1081/STA-120003646
DO - 10.1081/STA-120003646
M3 - Article
AN - SCOPUS:31244433378
SN - 0361-0926
VL - 31
SP - 665
EP - 681
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 5
ER -