文章基本信息

标题：Extended Generalized Skew-Elliptical Distributions and their Moments
作者：Zinoviy Landsman ; Udi Makov ; Tomer Shushi 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2017
卷号：79
期号：1
页码：76-100
DOI：10.1007/s13171-016-0090-2
语种：English
出版社：Indian Statistical Institute
摘要：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.
关键词：Extended skew-normal distribution ; Maximum likelihood equations ; Multivariate elliptical distributions ; Multivariate generalized skew-elliptical distributions ; Measurable map ; Radon-Nikodym derivative