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

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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 \(t>0\). 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.

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Acknowledgements

The authors are grateful to two anonymous referees for helpful comments that have resulted in an improved paper. Ehsan Zamanzade’s research was supported in part by Iran National Science Foundation (INSF).

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran

    Elham Zamanzade, Majid Asadi, Afshin Parvardeh & Ehsan Zamanzade

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  1. Elham Zamanzade
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  2. Majid Asadi
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  3. Afshin Parvardeh
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  4. Ehsan Zamanzade
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Correspondence to Ehsan Zamanzade.

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Zamanzade, E., Asadi, M., Parvardeh, A. et al. A ranked-based estimator of the mean past lifetime with an application. Stat Papers 64, 161–177 (2023). https://doi.org/10.1007/s00362-022-01314-y

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  • DOI: https://doi.org/10.1007/s00362-022-01314-y

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