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On moments of folded and truncated multivariate Student-t distributions based on recurrence relations

Author

Listed:
  • Christian E. Galarza

    (Escuela Superior Politécnica del Litoral, ESPOL)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

  • Wan-Lun Wang

    (Feng Chia University)

  • Víctor H. Lachos

    (University of Connecticut)

Abstract

The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:6:d:10.1007_s00184-020-00802-1
    DOI: 10.1007/s00184-020-00802-1
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    Cited by:

    1. Lin, Tsung-I & Wang, Wan-Lun, 2024. "On moments of truncated multivariate normal/independent distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    2. Tsung-I Lin & I-An Chen & Wan-Lun Wang, 2023. "A robust factor analysis model based on the canonical fundamental skew-t distribution," Statistical Papers, Springer, vol. 64(2), pages 367-393, April.
    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. Valeriano, Katherine A.L. & Galarza, Christian E. & Matos, Larissa A. & Lachos, Victor H., 2023. "Likelihood-based inference for the multivariate skew-t regression with censored or missing responses," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    5. Baishuai Zuo & Chuancun Yin, 2022. "Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures," Papers 2203.00839, arXiv.org.
    6. Christian E. Galarza & Larissa A. Matos & Victor H. Lachos, 2022. "An EM algorithm for estimating the parameters of the multivariate skew-normal distribution with censored responses," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 231-253, August.
    7. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering of multiply censored data via mixtures of t factor analyzers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 22-53, March.
    8. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.

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