Bivariate dependence, stochastic orders and conditional tails of the recurrence times in a renewal process

Losidis, Sotirios; Politis, Konstadinos; Psarrakos, Georgios

doi:10.15559/24-VMSTA266

Modern Stochastics: Theory and Applications

Bivariate dependence, stochastic orders and conditional tails of the recurrence times in a renewal process

Sotirios Losidis Konstadinos Politis

Georgios Psarrakos

https://doi.org/10.15559/24-VMSTA266

Pub. online: 12 November 2024 Type: Research Article

Open Access

Received
14 June 2024

Revised
17 October 2024

Accepted
17 October 2024

Published
12 November 2024

Abstract

The structure of dependence between the forward and the backward recurrence times in a renewal process is considered. Monotonicity properties, as a function of time, for the tail of the bivariate distribution for the recurrence times are discussed, as well as their link with aging properties of the interarrival distribution F. A necessary and sufficient condition for the renewal function to be concave is also obtained. Finally, some properties of the conditional tail for one of the two recurrence times, given some information on the other, are studied. The results are illustrated by some numerical examples.

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Keywords

Renewal process forward recurrence time backward recurrence time aging classes dependence positive regression dependence negative regression dependence upper orthant stochastic order

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60K05 60K10

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