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Technical Note—When Does the βth Percentile Residual Life Function Determine the Distribution?

Author

Listed:
  • Barry C. Arnold

    (University of California, Riverside, California)

  • Patrick L. Brockett

    (University of Texas, Austin, Texas)

Abstract

Knowledge of the βth percentile residual life function does not uniquely determine the underlying distribution. Additional information about the tail behavior of the distribution is needed. Knowledge of both the β 1 and β 2 percentile residual life functions does uniquely determine the distribution provided that β 1 and β 2 are noncommensurate. This corrects and extends the results of Schmittlein and Morrison (Schmittlein, D. C., D. G. Morrison. 1981. The median residual lifetime; a characterization theorem and an application. Opns. Res. 29 392–399.).

Suggested Citation

  • Barry C. Arnold & Patrick L. Brockett, 1983. "Technical Note—When Does the βth Percentile Residual Life Function Determine the Distribution?," Operations Research, INFORMS, vol. 31(2), pages 391-396, April.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:2:p:391-396
    DOI: 10.1287/opre.31.2.391
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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. 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.
    3. 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.

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