Further Monotonicity Properties for Specialized Renewal Processes
Copyright policy )Further Monotonicity Properties for Specialized Renewal Processes
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 E phi (z(t)) is increasing in t or = 0 for all increasing convex phi. 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). (Author)
60K05, 60J25, stochastically increasing, Renewal theory, Continuous-time Markov processes on general state spaces, IMRL and DFR distributions, monotonicity properties for stochastic processes, forward and backward recurrence times, increasing mean residual life
60K05, 60J25, stochastically increasing, Renewal theory, Continuous-time Markov processes on general state spaces, IMRL and DFR distributions, monotonicity properties for stochastic processes, forward and backward recurrence times, increasing mean residual life
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