On stochastic comparisons of excess times

Bruno Bassan, Yosef Rinott & Yehuda Vardi

A stationary renewal process based on iid random variables Xi 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 Xi's. We find necessary and sufficient conditions that explain this phenomenon, and related results on stochastic orderings arising from observations on renewal processes.

October, 2002
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