Moments of the Forward Recurrence Time in a Renewal Process

Sotirios Losidis () and Konstadinos Politis ()
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Sotirios Losidis: University of Piraeus
Konstadinos Politis: University of Piraeus

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 4, 1591-1600

Abstract: 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.

Keywords: Renewal function; Renewal density; Forward recurrence time; Increasing mean residual lifetime; Harmonic new better than used in expectation; Harmonic new worse than used in expectation; 60K05; 60K10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-018-9681-9

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