Full paper in PDF:
$% E. Gómez, M. Gómez-Villegas, and J. M. Marín, A survey on continuous elliptical vector distributions, Rev. Mat. Complut. 16 (2003), 345–361.%$

A Survey on Continuous Elliptical Vector Distributions

Eusebio GÓMEZ, Miguel GÓMEZ-VILLEGAS,
and J. Miguel MARíN
Departamento de Estadística e Investigación Operativa I
Universidad Complutense de Madrid
28040 Madrid — Spain
eusebio_gomez@mat.ucm.es
ma.gv@mat.ucm.es
ESCET, Universidad Rey Juan Carlos
28933 Móstoles (Madrid) — Spain
j.m.marin@escet.urjc.es

Received: March 14, 2001
 Accepted: May 8, 2002
ABSTRACT

In this paper it is taken up a revision and characterization of the class of absolutely continuous elliptical distributions upon a parameterization based on the density function. Their properties (probabilistic characteristics, affine transformations, marginal and conditional distributions and regression) are shown in a practical and easy to interpret way. Two examples are fully undertaken: the multivariate double exponential distribution and the multivariate uniform distribution.

Key words: elliptical distribution, ellipticaly contoured distribution, stochastic representation,conditional and marginal distributions, regression.
2000 Mathematics Subject Classification: 60E05, 62H05.