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Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data

Author

Listed:
  • Abdullah Fathi

    (Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt)

  • Al-Wageh A. Farghal

    (Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Ahmed A. Soliman

    (Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt)

Abstract

In this article, the estimation of the parameters and the reliability and hazard functions for Weibull inverted exponential (WIE) distribution is considered based on progressive first-failure censoring (PFFC) data. For non-Bayesian inference, maximum likelihood (ML) estimators are acquired; meanwhile, their existence is verified. Via asymptotic normality of ML estimators and delta method, the corresponding confidence intervals (CIs) of the parameters and the reliability and hazard functions are constructed. For Bayesian inference, Lindley’s approximation and Markov chain Monte Carlo (MCMC) techniques are proposed to obain the Bayes estimators and the corresponding credible intervals (CRIs). To this end, both symmetric and asymmetric loss functions are used. A large number of Monte Carlo simulations are implemented to evaluate the efficiency of the developed methods. Eventually, a numerical example is analyzed for illustrative purposes.

Suggested Citation

  • Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1648-:d:813833
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    References listed on IDEAS

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    1. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    2. Heba S. Mohammed & Saieed F. Ateya & Essam K. AL-Hussaini, 2017. "Estimation based on progressive first-failure censoring from exponentiated exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1479-1494, June.
    3. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    4. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
    5. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    6. Wu, Shuo-Jye & Huang, Syuan-Rong, 2012. "Progressively first-failure censored reliability sampling plans with cost constraint," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2018-2030.
    7. Yuge Du & Wenhao Gui, 2019. "Goodness of Fit Tests for the Log-Logistic Distribution Based on Cumulative Entropy under Progressive Type II Censoring," Mathematics, MDPI, vol. 7(4), pages 1-20, April.
    8. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    9. A. Bekker & J.J.J. Roux & P.J. Mosteit, 2000. "A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 29(7), pages 1419-1433, January.
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