Aging Renewal Point Processes and Exchangeability of Event Times

Fabio Vanni () and David Lambert
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Fabio Vanni: Department of Economics, University of Insubria, 21100 Varese, Italy
David Lambert: Department of Mathematics, University of North Texas, Denton, TX 76203-5017, USA

Mathematics, 2024, vol. 12, issue 10, 1-26

Abstract: In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. We prove that aging preserves the exchangeability of inter-arrival times. Our data analysis, which includes both surrogate data and a Bayesian approach to high-frequency currency exchange-rate data, shows how aging impacts key survival analysis metrics such as failure survival, renewal, and hazard rate functions.

Keywords: renewal processes; exchangeability; statistical aging; survival analysis; high frequency exchange rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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