ACTUARIAL ASPECTS OF HUMAN 

 LIFESPANS 



B. Benjamin 



General Register Office^ London 



Actuaries have always been profoundly interested in the 

 variation in the incidence of mortality with age since many of 

 their calculations of contingencies depend upon this variation. 

 The study of this age variation in mortality has given rise to 

 a number of hypothetical "laws" of mortality based on 

 theories about the exertion on the human body of deleterious 

 influences or about the wearing out of components of the body 

 and the exhaustion of living resources. These theories date 

 from Gompertz (1825) who argued on physiological grounds 

 that the intensity of mortality (in his terms the average 

 exhaustion of man's power to avoid death) gained equal pro- 

 portions in equal intervals of age and Makeham (1867) who 

 introduced a constant component as well as a logarithmically 

 increasing component of the force* of mortality as a reflection 



* It is necessary to define certain functions of the life-table : 



(1) Ix, the number still living at exact age out of an original generation 

 of Iq births (Iq is called the radix of the table). 



(2) dx, the number dying between exact ages x and x + 1 {= Ix — Iz+i) 



(3) px, the chance of surviving from exact age x to exact x + 1 



(4) qx, the chance of dying between exact age x and exact x + 1 



d-i 



i-t) 



Note: p^ + q^ = 1 



(5) [ix, the force of mortality. The concept is of an "instantaneous" 

 rate. It is approached by expressing the average rate of mortality 

 at age x (nix) over a finite interval of time as the ratio of (deaths at 

 age X in the interval) to (average population at age x in the interval) 



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