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Bayesian Estimation and Optimal Censoring of Inverted Generalized Linear Exponential Distribution Using Progressive First Failure Censoring

Author

Listed:
  • Mohamed A. W. Mahmoud

    (Al-Azhar University)

  • Mohamed G. M. Ghazal

    (Minia University
    Rustaq College of Education, Ministry of Higher Education)

  • Hossam M. M. Radwan

    (Minia University)

Abstract

This article studies the problem of statistical estimation and optimal censoring from three-parameter inverted generalized linear exponential distribution under progressive first failure censored samples. The maximum likelihood estimation is presented to estimate the unknown parameters. Approximate confidence interval is constructed to compute the interval estimation for the parameters and the delta method is used to compute the interval estimation for survival, hazard rate, and reversed hazard rate functions. The Gibbs sampler with the Metropolis-Hastings algorithm is applied to generate the Markov chain Monte Carlo samples from the posterior functions to approximate the Bayes estimation using several loss functions and to establish the symmetric credible interval for the parameters. A two real data sets are used to study the suggested censoring schemes and the optimal censoring is used to show the performance of the censoring schemes using maximum likelihood estimator and Bayes estimator. Also, a new vision is studied to obtain the optimal censoring using Bayes estimator under varying loss functions. Finally, a simulation study is presented to compare the different estimation methods based on mean square error and average absolute bias.

Suggested Citation

  • Mohamed A. W. Mahmoud & Mohamed G. M. Ghazal & Hossam M. M. Radwan, 2023. "Bayesian Estimation and Optimal Censoring of Inverted Generalized Linear Exponential Distribution Using Progressive First Failure Censoring," Annals of Data Science, Springer, vol. 10(2), pages 527-554, April.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:2:d:10.1007_s40745-020-00259-z
    DOI: 10.1007/s40745-020-00259-z
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    References listed on IDEAS

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    1. Singh, Umesh & Gupta, Pramod K. & Upadhyay, S. K., 2005. "Estimation of parameters for exponentiated-Weibull family under type-II censoring scheme," Computational Statistics & Data Analysis, Elsevier, vol. 48(3), pages 509-523, March.
    2. Amal S. Hassan & Marwa Abd-Allah, 2019. "On the Inverse Power Lomax Distribution," Annals of Data Science, Springer, vol. 6(2), pages 259-278, June.
    3. D. R. Barot & M. N. Patel, 2017. "Posterior analysis of the compound Rayleigh distribution under balanced loss functions for censored data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1317-1336, February.
    4. 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.
    5. Yao Zhang & William Q. Meeker, 2005. "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 237-249, June.
    6. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    7. Gunasekera, Sumith, 2018. "Inference for the Burr XII reliability under progressive censoring with random removals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 182-195.
    8. U. H. Salemi & S. Rezaei & Y. Si & S. Nadarajah, 2018. "On Optimal Progressive Censoring Schemes for Normal Distribution," Annals of Data Science, Springer, vol. 5(4), pages 637-658, December.
    9. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    10. Kyeongjun Lee & Youngseuk Cho, 2017. "Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 811-832, April.
    11. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
    12. M. S. Eliwa & M. El-Morshedy & Mohamed Ibrahim, 2019. "Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data," Annals of Data Science, Springer, vol. 6(2), pages 321-339, June.
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