Percentile Residual Life Functions

The α-percentile (0 < α < 1) residual life function at time t is defined as the α-percentile of the remaining life given survival up to time t. (Note that α-percentile is used in place of 100 α-percentile.) Two classes of life distributions defined by the α-percentile residual life function are the decreasing α-percentile residual life (DPRL-α) class and the new better than used with respect to the α-percentile (NBUP-α) class. These two classes are, respectively, analogous to the well-known decreasing mean residual life (DMRL) class and the new better than used in expectation (NBUE) class that involve the mean residual life function. We obtain properties of the α-percentile residual life function and of the DPRL-α, NBUP-α and their dual classes. Some results differ notably from corresponding results for the mean residual life function.