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Further Monotonicity Properties for Specialized Renewal Processes
The Annals of Probability
Vol. 9, No. 5 (Oct., 1981), pp. 891-895
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243747
Page Count: 5
You can always find the topics here!Topics: Mathematical monotonicity, Mathematical functions, Probabilities, Distributivity, Atoms, Laplace transformation
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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).
The Annals of Probability © 1981 Institute of Mathematical Statistics