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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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