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Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution

Author

Listed:
  • Hanan Haj Ahmad
  • Mukhtar M. Salah
  • M. S. Eliwa
  • Ziyad Ali Alhussain
  • Ehab M. Almetwally
  • Essam A. Ahmed

Abstract

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton–Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model.

Suggested Citation

  • Hanan Haj Ahmad & Mukhtar M. Salah & M. S. Eliwa & Ziyad Ali Alhussain & Ehab M. Almetwally & Essam A. Ahmed, 2022. "Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(12), pages 2981-3001, September.
    • Handle: RePEc:taf:japsta:v:49:y:2022:i:12:p:2981-3001
    DOI: 10.1080/02664763.2021.1931819
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    Cited by:

    1. Rajni Goel & Hare Krishna, 2024. "A study of accidental breakages in progressively type-ii censored lifetime experiments," 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. 15(6), pages 2105-2119, June.
    2. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.

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