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On moments of truncated multivariate normal/independent distributions

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  • Lin, Tsung-I
  • Wang, Wan-Lun

Abstract

Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate t, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository.

Suggested Citation

  • Lin, Tsung-I & Wang, Wan-Lun, 2024. "On moments of truncated multivariate normal/independent distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jmvana:v:199:y:2024:i:c:s0047259x23000945
    DOI: 10.1016/j.jmva.2023.105248
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    References listed on IDEAS

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    1. Ali Genç, 2013. "Moments of truncated normal/independent distributions," Statistical Papers, Springer, vol. 54(3), pages 741-764, August.
    2. Bulut, Y. Murat & Arslan, Olcay, 2015. "Matrix variate slash distribution," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 173-178.
    3. 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).
    4. Victor H. Lachos & Dipankar Bandyopadhyay & Dipak K. Dey, 2011. "Linear and Nonlinear Mixed-Effects Models for Censored HIV Viral Loads Using Normal/Independent Distributions," Biometrics, The International Biometric Society, vol. 67(4), pages 1594-1604, December.
    5. G. J. M. Rosa & D. Gianola & C. R. Padovani, 2004. "Bayesian Longitudinal Data Analysis with Mixed Models and Thick-tailed Distributions using MCMC," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 855-873.
    6. Lachos, Victor H. & Castro, Luis M. & Dey, Dipak K., 2013. "Bayesian inference in nonlinear mixed-effects models using normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 237-252.
    7. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, September.
    8. Victor H. Lachos & Celso R.B. Cabral & Carlos A. Abanto-Valle, 2012. "A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 531-549, July.
    9. 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.
    10. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
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