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On moments of doubly truncated multivariate normal mean–variance mixture distributions with application to multivariate tail conditional expectation

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  • Roozegar, Roohollah
  • Balakrishnan, Narayanaswamy
  • Jamalizadeh, Ahad

Abstract

Multivariate normal mean–variance mixture (NMVM) distributions are alternatives to the multivariate normal distribution when, in practice, we encounter data sets possessing large skewness and/or kurtosis measures. In this paper, we focus on truncated forms of NMVM distributions and derive explicit expressions for the first two moments. Our results are general which can be applied for any NMVM distribution. In particular, we derive explicit expressions for the first two moments of doubly truncated multivariate generalized hyperbolic (GH) distribution. We show that by using the results established here, the multivariate tail conditional expectation (MTCE) can be obtained for any NMVM distribution.

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  • Roozegar, Roohollah & Balakrishnan, Narayanaswamy & Jamalizadeh, Ahad, 2020. "On moments of doubly truncated multivariate normal mean–variance mixture distributions with application to multivariate tail conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:jmvana:v:177:y:2020:i:c:s0047259x19304087
    DOI: 10.1016/j.jmva.2019.104586
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    Cited by:

    1. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    2. Lin, Tsung-I & Wang, Wan-Lun, 2024. "On moments of truncated multivariate normal/independent distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Galarza, Christian E. & Matos, Larissa A. & Castro, Luis M. & Lachos, Victor H., 2022. "Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Baishuai Zuo & Chuancun Yin, 2022. "Doubly truncated moment risk measures for elliptical distributions," Papers 2203.01091, arXiv.org.
    5. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    6. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.

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