The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established and then their probabilistic properties, such as characteristic function, moments, quadratic forms as well as transformation properties, are investigated.

翻译：多元偏斜正态分布家族具有许多有趣的性质。本文证明这些性质同样适用于一般的偏斜椭圆分布类。针对此类分布，建立了若干随机表示，随后研究了其概率特征，包括特征函数、矩、二次型以及变换性质。