Percentile Residual Life Functions

摘要

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