IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v99y2016icp38-50.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316000025
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2016.01.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kehui Yao & Jun Zhu & Daniel J. O'Brien & Daniel Walsh, 2023. "Bayesian spatio‐temporal survival analysis for all types of censoring with application to a wildlife disease study," Environmetrics, John Wiley & Sons, Ltd., vol. 34(8), December.
    2. 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).
    3. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    2. 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.
    3. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    4. 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.
    5. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    6. 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.
    7. Emura, Takeshi & Shiu, Shau-Kai, 2014. "Estimation and model selection for left-truncated and right-censored lifetime data with application to electric power transformers analysis," MPRA Paper 57528, University Library of Munich, Germany.
    8. Sisi Chen & Fengkai Yang, 2023. "Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    9. Yandan Yang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2019. "Expectation–maximization algorithm for system-based lifetime data with unknown system structure," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 69-98, March.
    10. Gámiz Pérez, M. Luz & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2013. "Smoothing survival densities in practice," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 368-382.
    11. Semhar Michael & Tatjana Miljkovic & Volodymyr Melnykov, 2020. "Mixture modeling of data with multiple partial right-censoring levels," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 355-378, June.
    12. N. Davarzani & L. Golparvar & A. Parsian & R. Peeters, 2017. "Estimation on dependent right censoring scheme in an ordinary bivariate geometric distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1369-1384, June.
    13. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    14. Dijoux, Yann & Fouladirad, Mitra & Nguyen, Dinh Tuan, 2016. "Statistical inference for imperfect maintenance models with missing data," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 84-96.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:38-50. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.