12 Mean residual life: Theory and applications

Abstract

This chapter discusses the theory and applications of the mean residual life (MRL). MRL has been used as far back as the third century A.D. The MRL function is like the density function, the moment generating function, or the characteristic function: for a distribution with a finite mean, the MRL completely determines the distribution via an inversion formula. Not only is the MRL used for parametric modeling but also for nonparametric modeling. Large nonparametric classes of life distributions such as decreasing mean residual life (DMRL) and new better than used in expectation (NBUE) have been defined using MRL. Actuaries apply MRL to setting rates and benefits for life insurance. In the biomedical setting researchers analyze survivorship studies by MRL. IMRL distributions have been found useful as models in the social sciences for the lifelengths of wars and strikes. MRL functions occur naturally in other areas such as optimal disposal of an asset, renewal theory, dynamic programming, and branching processes. The chapter defines more formally the MRL function and surveys some of the key theory.