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Bayesian and classical inference in Maxwell distribution under adaptive progressively Type-II censored data

Author

Listed:
  • Anita Kumari

    (Central University of Haryana)

  • Kapil Kumar

    (Central University of Haryana)

  • Indrajeet Kumar

    (Kalasalingam Academy of Research and Education)

Abstract

In the reliability theory and life testing experiments, the Maxwell distribution has established a useful lifetime model due to its increasing failure rate property. To save time and money various types of censoring plans are studied in the literature. One such censoring scheme is adaptive progressive Type-II censoring (APT2C). It has recently become popular in life-testing experiments. The APT2C is a generalization of the progressive censoring scheme and it is very useful in various practical situations when testing material has a long life and high cost. This article deals with the problem of Bayesian and non-Bayesian estimation procedures of the unknown parameter and reliability characteristics of Maxwell distribution under the APT2C scheme. The maximum product spacing and the maximum likelihood estimates of the unknown parameters are obtained in the classical approach. In the Bayesian approach, the Bayes estimates are obtained under squared error loss function and linear exponential loss function with two choices of prior densities, non-informative and informative priors, respectively. The Bayes estimates are calculated using Tierney-Kadanae’s approximation and the Metropolis-Hastings algorithm. The asymptotic confidence interval, bootstrap confidence interval, and highest posterior density (HPD) credible interval are constructed for the interval estimation in the case of classical and Bayesian estimation procedures, respectively. Various estimates obtained in the theory are compared with the help of a Monte Carlo simulation study. Finally, a real data set is studied to show the applicability of the considered model.

Suggested Citation

  • Anita Kumari & Kapil Kumar & Indrajeet Kumar, 2024. "Bayesian and classical inference in Maxwell distribution under adaptive progressively Type-II censored data," 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(3), pages 1015-1036, March.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:3:d:10.1007_s13198-023-02185-8
    DOI: 10.1007/s13198-023-02185-8
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    References listed on IDEAS

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    1. Arak M. Mathai & Hans J. Haubold, 2018. "A generalized entropy optimization and Maxwell–Boltzmann distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(2), pages 1-10, February.
    2. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.
    3. 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.
    4. Shubham Saini & Sachin Tomer & Renu Garg, 2023. "Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(7), pages 1538-1567, May.
    5. Ajit Chaturvedi & Narendra Kumar & Kapil Kumar, 2018. "Statistical Inference for the Reliability Functions of a Family of Lifetime Distributions based on Progressive Type II Right Censoring," Statistica, Department of Statistics, University of Bologna, vol. 78(1), pages 81-101.
    6. 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.
    7. Kapil Kumar & Renu Garg & Hare Krishna, 2017. "Nakagami distribution as a reliability model under progressive censoring," 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. 8(1), pages 109-122, March.
    8. 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.
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