Mortality Deceleration at Extreme Old Age

Abstract

This paper clarifies the mortality deceleration at extreme old age in relation to the Gompertz function of mortality. It is noted that the Gompertz function of mortality as often discussed in the literature is actually composed of two mathematical formulations, one for the life table probability of dying qx and the other for the life table survival lx, the former being the rate of decrease of the latter. While Gompertz cautioned that the parameters for the mortality function q(x) = aq^x might be different for 3 or 4 broad age groups, this paper shows that the Gompertz function of survival l(x) = Ab^q^x fits well to the life table figures and the derived mortality q(x) = - Δ l(x) / l(x) displays a deceleration at extreme old age. Compared to the suggested modifications, the Gompertz function stands out in its robustness. It is further noted that the mortality statistics for very old ages can be deceiving. Given a modification in the declaration of statue death in Taiwan, the obvious deceleration of mortality at extreme old age has become less pronounced in recent years. It is suggested that the deceleration of mortality at extreme old age could be numerical rather than real.