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An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings

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Abstract

We establish an identity for \(Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) \), when \(\varvec{X}\) and \(\varvec{Y}\) both have matrix variate skew-normal distributions and the function f satisfies some weak conditions. The characteristic function of matrix variate skew normal distribution is then derived. We then make use of it to derive some necessary and sufficient conditions for the comparison of matrix variate skew-normal distributions under six different orders, such as usual stochastic order, convex order, increasing convex order, upper orthant order, directionally convex order and supermodular order.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This research was supported by the National Natural Science Foundation of China (No. 12071251, 11571198, 11701319).

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Authors and Affiliations

  1. School of Statistics, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Tong Pu & Chuancun Yin

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada

    Narayanaswamy Balakrishnan

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  1. Tong Pu
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  2. Narayanaswamy Balakrishnan
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  3. Chuancun Yin
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Correspondence to Chuancun Yin.

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Pu, T., Balakrishnan, N. & Yin, C. An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings. Commun. Math. Stat. 11, 629–647 (2023). https://doi.org/10.1007/s40304-021-00267-2

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  • DOI: https://doi.org/10.1007/s40304-021-00267-2

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