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An inferential analysis for the Weibull-G family of distributions under progressively censored data

Author

Listed:
  • Ashish Kumar Shukla

    (Ramanujan College, University of Delhi)

  • Sakshi Soni

    (University of Delhi)

  • Kapil Kumar

    (Central University of Haryana)

Abstract

In this article, the classical and the Bayesian estimators of the power of parameter and two reliability characteristics, say $$R(t)=P(X>t)$$ R ( t ) = P ( X > t ) and stress-strength reliability $$\mathcal {P}=P(X>Y)$$ P = P ( X > Y ) from the Weibull-G family of distributions are obtained using progressively Type-II censored data. The exact confidence intervals for the unknown parameter and both the reliability measures are also constructed under the same censoring, and the statistical testing procedures are developed for the parameter and $$\mathcal {P}$$ P . Afterward, we obtain the Bayes prediction intervals for future observations in a two-sample situation. We examine the behavior of these estimators under different censoring schemes using the Monte Carlo simulation technique. These estimators and prediction intervals are compared thoroughly, and comments are made based on their numerical values. Finally, we analyze two examples each having two real-life data sets for illustration purposes.

Suggested Citation

  • Ashish Kumar Shukla & Sakshi Soni & Kapil Kumar, 2023. "An inferential analysis for the Weibull-G family of distributions under progressively censored data," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1488-1524, September.
    • Handle: RePEc:spr:opsear:v:60:y:2023:i:3:d:10.1007_s12597-023-00645-0
    DOI: 10.1007/s12597-023-00645-0
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    References listed on IDEAS

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    1. 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.
    2. M. Mousa & Z. Jaheen, 2002. "Bayesian prediction for progressively censored data from the Burr model," Statistical Papers, Springer, vol. 43(4), pages 587-593, October.
    3. 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.
    4. Kousik Maiti & Suchandan Kayal, 2019. "Estimation for the generalized Fréchet distribution under progressive censoring scheme," 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. 10(5), pages 1276-1301, October.
    5. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    6. Ajit Chaturvedi & Renu Garg & Shubham Saini, 2022. "Estimation and testing procedures for the reliability characteristics of Kumaraswamy-G distributions based on the progressively first failure censored samples," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 494-517, June.
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