Stein’s lemma for truncated generalized skew-elliptical random vectors

• Main Authors: Baishuai Zuo, Chuancun Yin
• Format: Article
• Language: English
• Published: AIMS Press 2020-04-01
• Series: AIMS Mathematics
• Subjects: generalized skew-elliptical distributions; generalized skew-normal distributions; truncated random vectors; stein’s lemma
• Online Access: https://www.aimspress.com/article/10.3934/math.2020221/fulltext.html

Inspired by Shushi [1] and Adcock et al. [2], we consider Stein’s lemma for truncated generalized skew-elliptical random vectors. We provide two Stein’s lemmas. One is Stein’s lemma for truncated generalized skew-elliptical random vectors, the other is a special form of Stein’s lemma for truncated generalized skew-elliptical random vectors. Finally, the conditional tail expectation allocation, the lower-orthant conditional tail expectation at probability level q, the upper-orthant conditional tail expectation at probability level q, the truncated version of Wang’s premium, the multivariate tail conditional expectation and the multivariate tail covariance matrix as applications are given.