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A ranked-based estimator of the mean past lifetime with an application

Author

Listed:
  • Elham Zamanzade

    (University of Isfahan)

  • Majid Asadi

    (University of Isfahan)

  • Afshin Parvardeh

    (University of Isfahan)

  • Ehsan Zamanzade

    (University of Isfahan)

Abstract

The mean past lifetime (MPL) is an important tool in reliability and survival analysis for measuring the average time elapsed since the occurrence of an event, under the condition that the event has occurred before a specific time $$t>0$$ t > 0 . This article develops a nonparametric estimator for MPL based on observations collected according to ranked set sampling (RSS) design. It is shown that the proposed estimator is a strongly uniform consistent estimator of MPL. It is also proved that the introduced estimator tends to a Gaussian process under some mild conditions. A Monte Carlo simulation study is employed to evaluate the performance of the proposed estimator with its competitor in simple random sampling (SRS). Our findings show the introduced estimator is more efficient than its counterpart estimator in SRS as long as the quality of ranking is better than random. Finally, an illustrative example is provided to describe the potential application of the developed estimator in assessing the average time between the infection and diagnosis in HIV patients.

Suggested Citation

  • Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01314-y
    DOI: 10.1007/s00362-022-01314-y
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    References listed on IDEAS

    as
    1. Afshin Parvardeh, 2015. "A note on the asymptotic distribution of the estimation of the mean past lifetime," Statistical Papers, Springer, vol. 56(1), pages 205-215, February.
    2. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    3. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
    4. M. Mahdizadeh & Ehsan Zamanzade, 2018. "A new reliability measure in ranked set sampling," Statistical Papers, Springer, vol. 59(3), pages 861-891, September.
    5. Hani M. Samawi & Haresh Rochani & Daniel Linder & Arpita Chatterjee, 2017. "More efficient logistic analysis using moving extreme ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 753-766, March.
    6. Abdul Haq & Jennifer Brown & Elena Moltchanova & Amer Ibrahim Al‐Omari, 2013. "Partial ranked set sampling design," Environmetrics, John Wiley & Sons, Ltd., vol. 24(3), pages 201-207, May.
    7. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, October.
    8. Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.
    9. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.
    10. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    11. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.
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