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Estimation for the generalized Fréchet distribution under progressive censoring scheme

Author

Listed:
  • Kousik Maiti

    (National Institute of Technology Rourkela)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

Abstract

This paper takes into account the estimation of the unknown model parameters and the reliability characteristics for a generalized Fréchet distribution under progressive type-II censored sample. Maximum likelihood estimates are obtained. We calculate asymptotic confidence intervals and also compare in terms of their coverage probabilities for the unknown parameters, and the reliability and hazard rate functions. Further, Bayes estimates are derived with respect to various balanced type symmetric as well as asymmetric loss functions. Note that it is impossible to get the estimates in closed-form. So, we adopt importance sampling method in computing the Bayes estimates. Furthermore, we consider one-sample and two-sample prediction problems under Bayesian framework. In this case, the appropriate predictive intervals are proposed. Monte Carlo simulations are performed to observe the performance of various estimates. Moreover, results from simulation studies indicating the performance of the proposed methods are included. Finally, a real dataset is considered and analyzed for the illustration of the inferential procedures studied in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:5:d:10.1007_s13198-019-00875-w
    DOI: 10.1007/s13198-019-00875-w
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    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. 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.

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