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E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications

Author

Listed:
  • Hassan M. Okasha

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt)

  • Heba S. Mohammed

    (Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
    Department of Mathematics, Faculty of Science, New Valley University, El Kharga 72511, Egypt)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

Abstract

Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1261-:d:566237
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    References listed on IDEAS

    as
    1. Hassan M. Okasha & Chuanmei Wang & Jianhua Wang, 2020. "E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-13, February.
    2. L.F. Zhang & M. Xie & L.C. Tang, 2008. "On Weighted Least Squares Estimation for the Parameters of Weibull Distribution," Springer Series in Reliability Engineering, in: Hoang Pham (ed.), Recent Advances in Reliability and Quality in Design, chapter 3, pages 57-84, Springer.
    3. Zhang, Tieling & Xie, Min, 2011. "On the upper truncated Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 194-200.
    4. George C. Canavos & Chris P. Taokas, 1973. "Bayesian Estimation of Life Parameters in the Weibull Distribution," Operations Research, INFORMS, vol. 21(3), pages 755-763, June.
    5. 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.
    6. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
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