Sharp bounds for NBUE distributions

摘要

Let F be a new better than used in expectation (NBUE) distribution function with mean μ. In a previous paper (Brown in Probab. Eng. Inf. Sci. 20:195-230, 2006), the author derived the following bound. For any t ≥ μ,(-F)(t) = Pr(X≥t)≤e~(-∣t/μ-1∣).The main result of this paper is to show that this bound is sharp. Other sharp bounds for NBUE distributions are also derived.