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Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

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  • Sanjay Kumar Singh
  • Umesh Singh
  • Vikas Kumar Sharma

Abstract

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.

Suggested Citation

  • Sanjay Kumar Singh & Umesh Singh & Vikas Kumar Sharma, 2013. "Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme," Journal of Probability and Statistics, Hindawi, vol. 2013, pages 1-16, July.
    • Handle: RePEc:hin:jnljps:146140
    DOI: 10.1155/2013/146140
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    Cited by:

    1. Hassan M. Okasha & Heba S. Mohammed & Yuhlong Lio, 2021. "E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications," Mathematics, MDPI, vol. 9(11), pages 1-19, May.

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