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On variability of the mean remaining lifetime at random age

Author

Listed:
  • Majid Asadi

    (University of Isfahan)

  • Maxim Finkelstein

    (University of the Free State
    University of Strathclyde)

Abstract

In this short communication, we discuss the remaining lifetime and the mean remaining lifetime (MRL) of an item with a random age. We show that the MRL at random age is closely related to some well-known variability measures. First, we provide a decomposition result showing that the MRL at random age, similar to other variability measures, has a covariance representation. Under the proportional hazards (PH) model, we show that the MRL, depending on the parameter of proportionality, subsumes the Gini’s mean difference and the cumulative residual entropy as special cases. It is also shown that, under the PH model, the MRL can be expressed via the equilibrium distribution and the mean number of events in the generalized Pólya process.

Suggested Citation

  • Majid Asadi & Maxim Finkelstein, 2024. "On variability of the mean remaining lifetime at random age," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 717-730, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-023-00917-3
    DOI: 10.1007/s11749-023-00917-3
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    References listed on IDEAS

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    1. Majid Asadi, 2017. "A new measure of association between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 649-661, November.
    2. Marzieh Hashemi & Majid Asadi, 2021. "Optimal preventive maintenance of coherent systems: A generalized Pólya process approach," IISE Transactions, Taylor & Francis Journals, vol. 53(11), pages 1266-1280, November.
    3. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, April.
    4. Shlomo Yitzhaki & Edna Schechtman, 2005. "The properties of the extended Gini measures of variability and inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 401-433.
    5. Jorge Navarro, 2022. "Prediction of record values by using quantile regression curves and distortion functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 675-706, August.
    6. Nil Kamal Hazra & Maxim Finkelstein & Ji Hwan Cha, 2018. "Stochastic ordering for populations of manufactured items," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 173-196, March.
    Full references (including those not matched with items on IDEAS)

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