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On stochastic comparisons for population age and remaining lifetime

Author

Listed:
  • Ji Hwan Cha

    (Ewha Womans University)

  • Maxim Finkelstein

    (University of the Free State
    ITMO University)

Abstract

First, we consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these random variables are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we consider real populations of items that were incepted into operation (were born) at different instants of time and obtain some useful inequalities between the population age and the remaining lifetime using reasoning similar to that employed in population studies. We also discuss the aging properties of populations using different stochastic orders.

Suggested Citation

  • Ji Hwan Cha & Maxim Finkelstein, 2018. "On stochastic comparisons for population age and remaining lifetime," Statistical Papers, Springer, vol. 59(1), pages 199-213, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0759-6
    DOI: 10.1007/s00362-016-0759-6
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    References listed on IDEAS

    as
    1. James W. Vaupel, 2009. "Life lived and left: Carey’s equality," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(3), pages 7-10.
    2. Finkelstein, Maxim, 2013. "On some comparisons of lifetimes for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 300-304.
    3. Xiaohu Li & Maochao Xu, 2008. "Reversed hazard rate order of equilibrium distributions and a related aging notion," Statistical Papers, Springer, vol. 49(4), pages 749-767, October.
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    Cited by:

    1. Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.

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