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Percentile Residual Life Functions

Author

Listed:
  • Harry Joe

    (The Florida State University, Tallahassee, Florida)

  • Frank Proschan

    (The Florida State University, Tallahassee, Florida)

Abstract

The α-percentile (0 t is defined as the α-percentile of the remaining life given survival up to time t . (Note that α-percentile is used in place of 100 α-percentile.) Two classes of life distributions defined by the α-percentile residual life function are the decreasing α-percentile residual life (DPRL-α) class and the new better than used with respect to the α-percentile (NBUP-α) class. These two classes are, respectively, analogous to the well-known decreasing mean residual life (DMRL) class and the new better than used in expectation (NBUE) class that involve the mean residual life function. We obtain properties of the α-percentile residual life function and of the DPRL-α, NBUP-α and their dual classes. Some results differ notably from corresponding results for the mean residual life function.

Suggested Citation

  • Harry Joe & Frank Proschan, 1984. "Percentile Residual Life Functions," Operations Research, INFORMS, vol. 32(3), pages 668-678, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:668-678
    DOI: 10.1287/opre.32.3.668
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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. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    3. 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.
    4. Franco Pereira, Alba María & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2010. "Characterization of bathtub distributions via percentile residual life functions," DES - Working Papers. Statistics and Econometrics. WS ws102612, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. 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.
    6. Unnikrishnan Nair, N. & Vineshkumar, B., 2011. "Ageing concepts: An approach based on quantile function," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 2016-2025.
    7. Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2009. "New tests for exponentiality against new better than used in th quantile," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 85-97.
    8. 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.

    More about this item

    Keywords

    725 residual life of used items;

    Statistics

    Access and download statistics

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