Title: Extended Generalized Skew-Elliptical Distributions and their Moments

Author(s): Zinoviy Landsman, Udi Makov and Tomer Shushi
Issue: Volume 79 Series A Part 1 Year 2017
Pages: 76 -- 100
This paper constructs a family of multivariate distributions which extends the class of generalized skew-elliptical (GSE) distributions, introduced by Azzalini and Capitanio (${\it J. Roy. Statist. Soc. Ser. B}$, ${\bf 65}$, 367-389, 2003), and derives formulae for it’s characteristics; mean and covariance. The extended GSE family is particularly relevant whenever the need arises to model data by skewed distributions, as is the case in actuarial science, risk management and other branches of science. The paper also generalizes the skew-normal distribution in the sense of Azzalini and Dalla Valle (${\it Biometrika}$, ${\bf 83}$, 715-726, 1996). Furthermore, for estimation purposes, the maximum likelihood equations are derived. Finally, a numerical examples is provided which demonstrates that the extended GSE distribution offers a better fit in comparison to the GSE distribution.
AMS (2000) subject classification. Primary: 60 Exx, Secondary: 62Exx.
Keywords and phrases: Extended skew-normal distribution, Maximum likelihood equations, Multivariate elliptical distributions, Multivariate generalized skew-elliptical distributions, Measurable map, Radon-Nikodym derivative.