On ordered subpopulations and population mortality at advanced ages

We consider hazard (mortality) rates in heterogeneous populations consisting of ordered (in the defined stochastic sense) subpopulations. This setting can be interpreted via the fixed frailty models with one or more frailty parameters. The shape of the hazard rate is of main interest in this paper. Specifically, the deceleration and leveling off in the hazard rates (mortality plateaus) are discussed and some examples of lifetime distributions that can result in asymptotically flat hazard rates are considered. These examples are based on vitality models when an organism's initial vitality (resource) is 'consumed' in the course of life in accordance with a simple stochastic process (e.g., the Wiener process with drift or the gamma process).