Bounds for the Renewal Function and Related Quantities

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, 2022, vol. 24, issue 4, 2647-2660

Abstract: Abstract We obtain new bounds for the renewal function, as well as for the expected number of renewals over an interval $$(t,t+h]$$ ( t , t + h ] . Improved bounds are given when the interarrival distribution belongs to certain aging classes. Our results are compared with existing ones in the literature, both theoretically and with the aid of numerical resuts.

Keywords: Renewal function; Renewal equation; Lorden’s bound; Forward recurrence time; IFR; DFR; NBUE; IMRL; Bounds; 60K05; 60K10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-022-09953-2

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