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The Median Residual Lifetime: A Characterization Theorem and an Application

Author

Listed:
  • David C. Schmittlein

    (University of Pennsylvania, Philadelphia, Pennsylvania)

  • Donald G. Morrison

    (Columbia University, New York, New York)

Abstract

The concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart, the mean residual lifetime. A characterization theorem shows that a Pareto distribution of the second kind (or equivalently, a gamma mixture of exponentials) is the unique distribution with a linearly increasing median residual lifetime. An empirical example from the literature on strike durations is presented.

Suggested Citation

  • David C. Schmittlein & Donald G. Morrison, 1981. "The Median Residual Lifetime: A Characterization Theorem and an Application," Operations Research, INFORMS, vol. 29(2), pages 392-399, April.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:2:p:392-399
    DOI: 10.1287/opre.29.2.392
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    Citations

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    Cited by:

    1. Jong-Hyeon Jeong & Sin-Ho Jung & Joseph P. Costantino, 2008. "Nonparametric Inference on Median Residual Life Function," Biometrics, The International Biometric Society, vol. 64(1), pages 157-163, March.
    2. Shaked, Moshe, 2010. "The decreasing percentile residual life aging notion," DES - Working Papers. Statistics and Econometrics. WS ws101807, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Yixin Wang & Ying Qing Chen, 2019. "Estimating Attributable Life Expectancy Under the Proportional Mean Residual Life Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 659-676, December.
    4. Zhao, Mu & Jiang, Hongmei, 2015. "Berry–Esseen bounds for the percentile residual life function estimators," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 133-140.
    5. Sin-Ho Jung & Jong-Hyeon Jeong & Hanna Bandos, 2009. "Regression on Quantile Residual Life," Biometrics, The International Biometric Society, vol. 65(4), pages 1203-1212, December.
    6. Yimeng Liu & Liwen Wu & Gong Tang & Abdus S. Wahed, 2023. "A series of two-sample non-parametric tests for quantile residual life time," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 234-252, January.
    7. Rosa E. Lillo, 2005. "On the median residual lifetime and its aging properties: A characterization theorem and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 370-380, June.
    8. Ruosha Li & Xuelin Huang & Jorge Cortes, 2016. "Quantile residual life regression with longitudinal biomarker measurements for dynamic prediction," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 755-773, November.
    9. M. Kayid & M. Shafaei Noughabi & A. M. Abouammoh, 2020. "A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 237-253, April.

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