The Median Residual Lifetime: A Characterization Theorem and an Application

The concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart, the mean residual lifetime. A characterization theorem shows that a Pareto distribution of the second kind (or equivalently, a gamma mixture of exponentials) is the unique distribution with a linearly increasing median residual lifetime. An empirical example from the literature on strike durations is presented.