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Moments of the Forward Recurrence Time in a Renewal Process

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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.

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Authors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli, Demetriou Str, Piraeus, 18534, Greece

    Sotirios Losidis & Konstadinos Politis

Authors
  1. Sotirios Losidis
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  2. Konstadinos Politis
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Correspondence to Sotirios Losidis.

Additional information

This work has been partly supported by the University of Piraeus Research Center.

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Losidis, S., Politis, K. Moments of the Forward Recurrence Time in a Renewal Process. Methodol Comput Appl Probab 22, 1591–1600 (2020). https://doi.org/10.1007/s11009-018-9681-9

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  • DOI: https://doi.org/10.1007/s11009-018-9681-9

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