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Modern Stochastics: Theory and Applications


Bivariate dependence, stochastic orders and conditional tails of the recurrence times in a renewal process
Volume 12, Issue 2 (2025), pp. 153–167
Pub. online: 12 November 2024      Type: Research Article      Open accessOpen 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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© 2025 The Author(s). Published by VTeX
Open access article under the CC BY license.

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

MSC2020
60K05 60K10

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