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Further Monotonicity Properties for Specialized Renewal Processes

Mark Brown
The Annals of Probability
Vol. 9, No. 5 (Oct., 1981), pp. 891-895
Stable URL: http://www.jstor.org/stable/2243747
Page Count: 5
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Further Monotonicity Properties for Specialized Renewal Processes
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Abstract

Define Z(t) to be the forward recurrence time at t for a renewal process with interarrival time distribution, F, which is assumed to be IMRL (increasing mean residual life). It is shown that Eφ(Z(t)) is increasing in t ≥ 0 for all increasing convex φ. An example demonstrates that Z(t) is not necessarily stochastically increasing nor is the renewal function necessarily concave. Both of these properties are known to hold for F DFR (decreasing failure rate).

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