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Point and interval estimation of quantiles of several exponential populations with a common location under progressive censoring scheme

Author

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  • Habiba Khatun

    (National Institute of Technology Rourkela)

  • Manas Ranjan Tripathy

    (National Institute of Technology Rourkela)

Abstract

We consider the problems of point, and interval estimation of the $$p\textrm{th}$$ p th quantile of the first population when progressive type-II censored samples are available from several exponential populations with a common location, and different scale parameters. First, in the case of point estimation, we derive the maximum likelihood estimator, a modification to it and the uniformly minimum variance unbiased estimator (UMVUE) of the quantile. An estimator dominating the UMVUE is derived. Further, a class of affine equivariant estimators is derived, and an inadmissibility result is proved. Consequently, improved estimators dominating the UMVUE are derived. In the case of interval estimation, several confidence intervals, such as generalized confidence interval, bootstrap confidence interval, and the highest posterior density confidence interval, are obtained for the quantile. The point estimators are compared through the risk values, whereas the interval estimators are compared through coverage probability and average length using a simulation study numerically. The conclusions regarding their performances have been made based on our simulation study. Finally, a real-life data set has been considered for illustrative purposes.

Suggested Citation

  • Habiba Khatun & Manas Ranjan Tripathy, 2024. "Point and interval estimation of quantiles of several exponential populations with a common location under progressive censoring scheme," Computational Statistics, Springer, vol. 39(4), pages 2217-2257, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01410-z
    DOI: 10.1007/s00180-023-01410-z
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    References listed on IDEAS

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    1. Nabakumar Jana & Somesh Kumar & Kashinath Chatterjee, 2016. "Bayes estimation for exponential distributions with common location parameter and applications to multi-state reliability models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2697-2712, November.
    2. K. Krishnamoorthy & Yanping Xia, 2018. "Confidence intervals for a two-parameter exponential distribution: One- and two-sample problems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(4), pages 935-952, February.
    3. Huang, Li-Fei & Johnson, Richard A., 2006. "Confidence regions for the ratio of percentiles," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 384-392, February.
    4. repec:dau:papers:123456789/1908 is not listed on IDEAS
    5. Kumar, Somesh & Sharma, Divakar, 1996. "A note on estimating quantiles of exponential populations," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 115-118, February.
    6. Willem Albers & Peter Löhnberg, 1984. "An Approximate Confidence Interval For The Difference Between Quantiles In A Bio‐Medical Problem," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(1), pages 20-22, March.
    7. N. Balakrishnan & A. J. Hayter & W. Liu & S. Kiatsupaibul, 2015. "Confidence Intervals for Quantiles of a Two-parameter Exponential Distribution under Progressive Type-II Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 3001-3010, July.
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