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Bayesian inference of Weibull distribution based on left truncated and right censored data

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  • Kundu, Debasis
  • Mitra, Debanjan

Abstract

This article deals with the Bayesian inference of the unknown parameters of the Weibull distribution based on the left truncated and right censored data. It is assumed that the scale parameter of the Weibull distribution has a gamma prior. The shape parameter may be known or unknown. If the shape parameter is unknown, it is assumed that it has a very general log-concave prior distribution. When the shape parameter is unknown, the closed form expression of the Bayes estimates cannot be obtained. We propose to use Gibbs sampling procedure to compute the Bayes estimates and the associated highest posterior density credible intervals. Two data sets, one simulated and one real life, have been analyzed to show the effectiveness of the proposed method, and the performances are quite satisfactory. We further develop posterior predictive density of an item still in use. Based on the predictive density we provide predictive survival probability at a certain point along with the associated highest posterior density credible interval and also the expected number of failures in a given interval.

Suggested Citation

  • Kundu, Debasis & Mitra, Debanjan, 2016. "Bayesian inference of Weibull distribution based on left truncated and right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 38-50.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:38-50
    DOI: 10.1016/j.csda.2016.01.001
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    References listed on IDEAS

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    1. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
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    Cited by:

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    2. Wassim R. Abou Ghaida & Ayman Baklizi, 2022. "Prediction of future failures in the log-logistic distribution based on hybrid censored data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(4), pages 1598-1606, August.
    3. Shuto, Susumu & Amemiya, Takashi, 2022. "Sequential Bayesian inference for Weibull distribution parameters with initial hyperparameter optimization for system reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    4. Kundu, Debasis & Mitra, Debanjan & Ganguly, Ayon, 2017. "Analysis of left truncated and right censored competing risks data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 12-26.
    5. Zhiyuan Zuo & Liang Wang & Yuhlong Lio, 2022. "Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations," Energies, MDPI, vol. 16(1), pages 1-25, December.
    6. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    7. Xifan Song & Ziyu Xiong & Wenhao Gui, 2022. "Parameter Estimation of Exponentiated Half-Logistic Distribution for Left-Truncated and Right-Censored Data," Mathematics, MDPI, vol. 10(20), pages 1-26, October.

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