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Aging Renewal Point Processes and Exchangeability of Event Times

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-27, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1529-:d:1394477
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    References listed on IDEAS

    as
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