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Properties and Estimations of a Multivariate Folded Normal Distribution

Author

Listed:
  • Xi Liu

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

  • Yiqiao Jin

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
    School of Data Science, Fudan University, Shanghai 200433, China)

  • Yifan Yang

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
    Transwarp Technology (Shanghai) Co., Ltd., Shanghai 200233, China)

  • Xiaoqing Pan

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

Abstract

A multivariate folded normal distribution is a distribution of the absolute value of a Gaussian random vector. In this paper, we provide the marginal and conditional distributions of the multivariate folded normal distribution, and also prove that independence and non-correlation are equivalent for it. In addition, we provide a numerical approach using the R language to fit a multivariate folded normal distribution. The accuracy of the estimated mean and variance parameters is then examined. Finally, a real data application to body mass index data are presented.

Suggested Citation

  • Xi Liu & Yiqiao Jin & Yifan Yang & Xiaoqing Pan, 2023. "Properties and Estimations of a Multivariate Folded Normal Distribution," Mathematics, MDPI, vol. 11(23), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4860-:d:1293437
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    References listed on IDEAS

    as
    1. Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
    2. Yao, Jia & Lou, Bendong & Pan, Xiaoqing, 2023. "Characterizations of stochastic ordering for non-negative random variables," Statistics & Probability Letters, Elsevier, vol. 203(C).
    3. Psarakis, Stelios & Panaretos, John, 2001. "On Some Bivariate Extensions of the Folded Normal and the Folded-T Distributions," MPRA Paper 6383, University Library of Munich, Germany.
    4. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
    5. Vytaras Brazauskas & Andreas Kleefeld, 2011. "Folded and log-folded- distributions as models for insurance loss data," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2011(1), pages 59-74.
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