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On the property of multivariate generalized hyperbolic distribution and the Stein-type inequality

Author

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  • Xiang Deng
  • Jing Yao

Abstract

This note consists of two parts . In the first part, we provide a pedagogic review on the multivariate generalized hyperbolic (MGH) distribution. We show that this probability family is close under margining, conditioning, and linear transforms; however, such property does not hold for its subclasses. In the second part, we obtain the Stein-type inequality in the context of MGH distribution. Moreover, we apply the Stein-type inequality to prove a lower bound for Var[h(X)]. Particularly, we present examples when X belongs to some well-known subclasses in MGH family.

Suggested Citation

  • Xiang Deng & Jing Yao, 2018. "On the property of multivariate generalized hyperbolic distribution and the Stein-type inequality," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5346-5356, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:21:p:5346-5356
    DOI: 10.1080/03610926.2017.1390134
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    Cited by:

    1. Xiangyu Han & Chuancun Yin, 2022. "Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions," Mathematics, MDPI, vol. 10(4), pages 1-21, February.

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