Some stochastic orderings of multivariate skew-normal random vectors

Xueyan Li; Chuancun Yin; Xueyan Li; Chuancun Yin

doi:10.3934/math.20231190

AIMS Mathematics

2023, Volume 8, Issue 10: 23427-23441. doi: 10.3934/math.20231190

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Research article

Some stochastic orderings of multivariate skew-normal random vectors

Xueyan Li ,
Chuancun Yin ^,

School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China

Received: 26 May 2023 Revised: 15 July 2023 Accepted: 19 July 2023 Published: 26 July 2023
MSC : 60E10, 60E15

In this paper, we investigate some multivariate integral stochastic orderings of skew-normal random vectors. We derive the results of the sufficient and/or necessary conditions by applying an identity for $ Ef({\mathbf Y})-Ef({\mathbf X}) $, where $ {\mathbf X} $ and $ {\mathbf Y} $ are multivariate skew-normal random vectors, $ f $ satisfies some weak regularity condition. The integral orders considered here are the componentwise convex, copositive, completely-positive orderings and their corresponding increasing ones as well as linear forms of stochastic orderings, which play a vital role in transforming the unmanageable multivariate components into an easy-to-handle univariate variable.
- componentwise convex ordering,
- completely-positive ordering,
- copositive ordering,
- integral stochastic ordering,
- linear ordering,
- multivariate skew-normal
Citation: Xueyan Li, Chuancun Yin. Some stochastic orderings of multivariate skew-normal random vectors[J]. AIMS Mathematics, 2023, 8(10): 23427-23441. doi: 10.3934/math.20231190

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Abstract

In this paper, we investigate some multivariate integral stochastic orderings of skew-normal random vectors. We derive the results of the sufficient and/or necessary conditions by applying an identity for $ Ef({\mathbf Y})-Ef({\mathbf X}) $, where $ {\mathbf X} $ and $ {\mathbf Y} $ are multivariate skew-normal random vectors, $ f $ satisfies some weak regularity condition. The integral orders considered here are the componentwise convex, copositive, completely-positive orderings and their corresponding increasing ones as well as linear forms of stochastic orderings, which play a vital role in transforming the unmanageable multivariate components into an easy-to-handle univariate variable.

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