Sharp upper bounds for the mean residual waiting time of records

摘要

Along with the failure rate, the mean residual life function has received considerable attention in reliability theory, survival analysis and risk studies. In the context of records, we present sharp upper bounds for the mean residual waiting time of the nth value of kth records from a sequence of identically independent distributed random variables. The bounds are evaluated in terms of location and scale units of the residual lifetime at t, X_t - X - t|X > t. We then characterize the probability distributions for which the bounds are attained. Evaluations of the resulting bounds for various choices of n and k are also presented.