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

Baishuai Zuo; Chuancun Yin; Baishuai Zuo; Chuancun Yin

doi:10.3934/math.2020221

AIMS Mathematics

2020, Volume 5, Issue 4: 3423-3433. doi: 10.3934/math.2020221

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Research article

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

Baishuai Zuo ,
Chuancun Yin ^,

School of Statistics, Qufu Normal University, Qufu 273165, Shandong, China

Received: 20 February 2020 Accepted: 30 March 2020 Published: 02 April 2020
MSC : 62E10, 62H05

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.
- generalized skew-elliptical distributions,
- generalized skew-normal distributions,
- truncated random vectors,
- Stein’s lemma
Citation: Baishuai Zuo, Chuancun Yin. Stein’s lemma for truncated generalized skew-elliptical random vectors[J]. AIMS Mathematics, 2020, 5(4): 3423-3433. doi: 10.3934/math.2020221

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Abstract

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.

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