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Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions

Author

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  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Faten S. Alamri

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Ehab M. Almetwally

    (Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt)

  • Min Wang

    (Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA)

  • Hoda Rezk

    (Department of Statistics, Al-Azhar University, Cairo 11751, Egypt)

Abstract

Accelerated life testing (ALT) is a time-saving technology used in a variety of fields to obtain failure time data for test units in a fraction of the time required to test them under normal operating conditions. This study investigated progressive-stress ALT with progressive type II filtering with the lifetime of test units following a Nadarajah–Haghighi (NH) distribution. It is assumed that the scale parameter of the distribution obeys the inverse power law. The maximum likelihood estimates and estimated confidence intervals for the model parameters were obtained first. The Metropolis–Hastings (MH) algorithm was then used to build Bayes estimators for various squared error loss functions. We also computed the highest posterior density (HPD) credible ranges for the model parameters. Monte Carlo simulations were used to compare the outcomes of the various estimation methods proposed. Finally, one data set was analyzed for validation purposes.

Suggested Citation

  • Refah Alotaibi & Faten S. Alamri & Ehab M. Almetwally & Min Wang & Hoda Rezk, 2022. "Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1602-:d:811076
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    References listed on IDEAS

    as
    1. Sang-Jun Park & Bong-Jin Yum, 1998. "Optimal design of accelerated life tests under modified stress loading methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 41-62.
    2. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
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    4. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    5. Refah Alotaibi & Mervat Khalifa & Ehab M. Almetwally & Indranil Ghosh & Rezk. H. & Markos Koutras, 2021. "Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model," Journal of Mathematics, Hindawi, vol. 2021, pages 1-20, October.
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