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Moments of the Forward Recurrence Time in a Renewal Process

Author

Listed:
  • Sotirios Losidis

    (University of Piraeus)

  • Konstadinos Politis

    (University of Piraeus)

Abstract

The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability of the forward recurrence time (as measured by the variance or the standard deviation) is important especially when we want to predict when the next event will occur. In this paper we study the moments of the forward recurrence time in a renewal process. In particular, we discuss the monotonicity of the variance for these recurrence times and study the covariance between the forward recurrence time at t and the number of renewals over [0,t]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing.

Suggested Citation

  • Sotirios Losidis & Konstadinos Politis, 2020. "Moments of the Forward Recurrence Time in a Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1591-1600, December.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-018-9681-9
    DOI: 10.1007/s11009-018-9681-9
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    References listed on IDEAS

    as
    1. Losidis, Sotirios & Politis, Konstadinos, 2017. "A two-sided bound for the renewal function when the interarrival distribution is IMRL," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 164-170.
    2. Coleman, Rodney, 1982. "The moments of forward recurrence time," European Journal of Operational Research, Elsevier, vol. 9(2), pages 181-183, February.
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