Tail densities of skew-elliptical distributions
Tail densities of skew-elliptical distributions
复制标题
斜椭圆分布的尾部密度
DOI：
10.1016/j.jmva.2019.01.009
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Haijun Li
中科院分区：
文献类型：
--
作者：
H. Joe;Haijun Li
偏椭圆分布构成了一大类多元分布，它们既考虑了偏度又考虑了各种尾部特性。这类有更简单的表示在密度方面，而不是累积分布函数，和尾部密度的方法以前已经开发研究尾部属性时，多元密度有更容易处理的形式。特殊的斜椭圆结构允许推导出特定形式的尾部密度为那些斜椭圆copula，承认概率密度函数，密度发生器上的重尾和轻尾条件下。偏椭圆copula的尾部密度是显式的，并且仅依赖于底层密度生成元的尾部性质和偏度参数的条件。在重尾情形下，偏度参数对偏椭圆copula尾密度的影响比在轻尾情形下更大，而在轻尾情形下，偏椭圆copula尾密度只与对称椭圆copula尾密度成正比.各种例子，包括尾部密度的偏态正态分布和偏态t分布，给出。
Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative distribution functions, and the tail density approach has previously been developed to study tail properties when multivariate densities have more tractable forms. The special skew-elliptical structure allows for derivations of specific forms for the tail densities for those skew-elliptical copulas that admit probability density functions, under heavy and light tail conditions on density generators. The tail densities of skew-elliptical copulas are explicit and depend only on tail properties of the underlying density generator and conditions on the skewness parameters. In the heavy-tail case skewness parameters affect tail densities of the skew-elliptical copulas more profoundly than that in the light tail case, whereas in the latter case the tail densities of skew-elliptical copulas are only proportional to the tail densities of symmetrical elliptical copulas. Various examples, including tail densities of skew-normal and skew-t distributions, are given.
DOI：
10.1017/cbo9781139248891
发表时间：
2018-03
期刊：
--
影响因子：
--
作者：
A. Azzalini;A. Capitanio
通讯作者：
A. Azzalini;A. Capitanio