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On independence of time and cause

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  • Kella, Offer

Abstract

For two independent, almost surely finite random variables, independence of their minimum (time) and the events that either one of them is equal to the minimum (cause) is completely characterized. It is shown that, other than for trivial cases where, almost surely, either one random variable is strictly greater than the other or one is a constant and the other is greater than or equal to it, this happens if and only if both random variables are distributed like the same strictly increasing function of two independent random variables, where either both are exponentially distributed or both are geometrically distributed. This is then generalized to the multivariate case.

Suggested Citation

  • Kella, Offer, 2024. "On independence of time and cause," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001682
    DOI: 10.1016/j.spl.2023.109944
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    References listed on IDEAS

    as
    1. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    2. W. R. Allen, 1963. "Letter to the Editor---A Note on Conditional Probability of Failure When Hazards are Proportional," Operations Research, INFORMS, vol. 11(4), pages 658-659, August.
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