The actuaries including Gompertz himself first noted this phenomenon of mortality deceleration. They also proposed a logistic formula for fitting mortality growth with age in order to account for mortality fall-off at advanced ages (Perks, 1932; Beard,
1959, 1971). Robert Eric Beard (1959) introduced a model of population heterogeneity with gamma distributed individual risk in order to explain mortality deceleration at older ages. This explanation is the most common explanation of mortality deceleration now.