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Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering

Author

Listed:
  • Refah Alotaibi

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

  • Mazen Nassar

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt)

  • Ahmed Elshahhat

    (Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt)

Abstract

This work addresses the estimation issues of the XLindley distribution using an adaptive Type-II progressive hybrid censoring scheme. Maximum likelihood and Bayesian approaches are used to estimate the unknown parameter, reliability, and hazard rate functions. Bayesian estimators are explored under the assumption of independent gamma priors and a symmetric loss function. The approximate confidence intervals and the highest posterior density credible intervals are also computed. An extensive simulation study that takes into account various sample sizes and censoring schemes is implemented to evaluate the various estimating methods. Finally, for an explanation, two real data sets from the chemical engineering field are provided to show that the XLindley distribution is the best model compared to some competitive models for the same real data. The Bayesian paradigm utilizing the Metropolis–Hastings algorithm to generate samples from the posterior distribution is recommended to estimate any parameter of life of the XLindley distribution when data are obtained from adaptive Type-II progressively hybrid censored sample.

Suggested Citation

  • Refah Alotaibi & Mazen Nassar & Ahmed Elshahhat, 2022. "Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3355-:d:915958
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    References listed on IDEAS

    as
    1. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    2. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    3. Mazen Nassar & Refah Alotaibi & Sanku Dey & Leonardo Acho, 2022. "Estimation Based on Adaptive Progressively Censored under Competing Risks Model with Engineering Applications," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-13, March.
    4. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    5. 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.
    6. 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.
    7. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
    8. Pavia, Jose M., 2015. "Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(c01).
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    Cited by:

    1. Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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