Extended Generalized Skew-Elliptical Distributions and their Moments

Zinoviy Landsman (), Udi Makov () and Tomer Shushi ()
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Zinoviy Landsman: University of Haifa
Udi Makov: University of Haifa
Tomer Shushi: University of Haifa

Sankhya A: The Indian Journal of Statistics, 2017, vol. 79, issue 1, No 4, 76-100

Abstract: Abstract This paper constructs a family of multivariate distributions which extends the class of generalized skew-elliptical (GSE) distributions, introduced by Azzalini and Capitanio (J. Roy. Statist. Soc. Ser. B, 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 (Biometrika, 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.

Keywords: Extended skew-normal distribution; Maximum likelihood equations; Multivariate elliptical distributions; Multivariate generalized skew-elliptical distributions; Measurable map; Radon-Nikodym derivative; Primary: 60 Exx; Secondary: 62Exx (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13171-016-0090-2

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