Estimation of distributions with the new better than used in expectation property

A lifetime XX with survival function SS, mean residual life function (MRL) MM, and finite mean μμ is said to be new better than used in expectation (NBUE) if M(t)≤μM(t)≤μ for all t≥0t≥0. We propose a new estimator for SS, based on a natural estimator of MM defined under the NBUE restriction. This is much simpler to implement than the only other restricted estimator in the literature. We also derive some asymptotic properties of the MRL of XX and extend our results to the censored case.