Shaun S. Wang and Robert L. Brown
Abstract
Based on the everyday observations that individual human beings vary significantly in their capacity to combat death, we adopt a so-called frailty model of human mortality. This frailty model assumes that each individual in a given population is endowed with his or her own frailty index, r, which remains constant for life. In addition, we assume that the individual's force of mortality (hazard rate function) at age x, mu_x (r), satisfies mu_x (r) = r where mu_x is the population's base force of mortality at age x. Given the probability distribution of the frailty index among the newborns in the population, an expression is given for the distribution of the frailty index among the survivors reaching age x in the population. Finally, assuming that (i) the rate of mortality improvement for any age is proportional to the average frailty level of the individuals at that age, (ii) a gamma distribution for the frailty index, and (iii) a Gompertz form for the population's base force of mortality, we graduate (smooth) the observed mortality improvement factors in the published Society of Actuaries' GAR-94 Table.
Key words and phrases: force of mortality, hazard rate, gamma distribution, Gompertz law
Shaun S. Wang