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Nonparametric Predictive Inference for Discrete Lifetime Data

Author

Listed:
  • Frank P. A. Coolen

    (Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK)

  • Tahani Coolen-Maturi

    (Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK)

  • Ali M. Y. Mahnashi

    (Department of Mathematics, College of Science, Jazan University, Jazan 45 142, Saudi Arabia)

Abstract

This paper presents nonparametric predictive inference for discrete lifetime data. While lifetimes are mostly treated as continuous random variables in statistics, there are scenarios where time observations are recorded as discrete values, for example, in actuary, where lifetimes are often recorded as integers in years. The presented method provides lower and upper probabilities for a variety of events of interest involving discrete lifetimes, with examples provided for illustration. Furthermore, the discrete-time situation is considered for inference of the reliability of systems, with discrete-time data for components of different types and using the survival signature to combine inference on components’ reliability to quantify the overall system reliability.

Suggested Citation

  • Frank P. A. Coolen & Tahani Coolen-Maturi & Ali M. Y. Mahnashi, 2024. "Nonparametric Predictive Inference for Discrete Lifetime Data," Mathematics, MDPI, vol. 12(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3514-:d:1518113
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    References listed on IDEAS

    as
    1. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2015. "Predictive inference for system reliability after common-cause component failures," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 27-33.
    2. Coolen, F.P.A. & Coolen-Schrijner, P., 2006. "Nonparametric predictive subset selection for proportions," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1675-1684, September.
    3. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, March.
    4. Janurová, Kateřina & Briš, Radim, 2014. "A nonparametric approach to medical survival data: Uncertainty in the context of risk in mortality analysis," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 145-152.
    5. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
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