On stochastic comparisons of excess times

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On stochastic comparisons of excess times

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Bruno Bassan
Yosef Rinott ()
Yehuda Vardi

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Yosef Rinott

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.

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Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp302.

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Length: 10 pages
Date of creation: Oct 2002
Date of revision:
Handle: RePEc:huj:dispap:dp302

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This paper has been announced in the following NEP Reports:

NEP-ALL-2003-05-15 (All new papers)
NEP-ECM-2003-05-16 (Econometrics)

References listed on IDEAS
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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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)

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