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On stochastic comparisons of excess times

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  • Bruno Bassan
  • Yosef Rinott
  • Yehuda Vardi

Abstract

A stationary renewal process based on iid random variables $X_i$ is observed at a given time. The excess time, that is, the residual time until the next renewal event, is of course smaller than the total current $X$ which consists of the residual time plus the current age. Nevertheless in certain types of data the distribution of the excess times is stochastically larger than that of $X_i$'s. We find necessary and sufficient conditions that explain this phenomenon, and related results on stochastic orderings arising from observations on renewal processes.

Suggested Citation

  • Bruno Bassan & Yosef Rinott & Yehuda Vardi, 2002. "On stochastic comparisons of excess times," Discussion Paper Series dp302, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp302
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp302.pdf
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    References listed on IDEAS

    as
    1. Bon, Jean-Louis & Illayk, Abbas, 2002. "A note on some new renewal ageing notions," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 151-155, April.
    2. Abouammoh, A. M. & Ahmed, A. N., 1992. "On renewal failure rate classes of life distributions," Statistics & Probability Letters, Elsevier, vol. 14(3), pages 211-217, June.
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