Actuarial Aspects of Human Lifespans 



approximation to the curve of deaths {d^ is of course discon- 

 tinuous while the "curve of deaths" is continuous. It has been 

 assumed that d^ = [i^^:^.!^^^). The curve has then been treated 

 from its later mode (e.g. the peak at age 76 in Fig. 3) to the 

 upper limit of age as the right-hand side of the distribution of 

 "senescent" deaths, i.e. of normal lifespans, and the left-hand 



Fig. 1. Curve of deaths. English Life-Table No. 1. 1841. Males. 



total deaths 



senescent deaths 



— — — — — — . — . anticipated deaths 



side of this distribution has been drawn in (broken line in the 

 figures) to exactly mirror the right-hand side. It is thus 

 assumed (unlike Clarke) that the biometric distribution of 

 lifespans is symmetrical. When the deaths of this left-hand 

 side of the distribution are subtracted from the main curve of 

 deaths the residual (of "anticipated" deaths) tails off (by a 

 broken line in Fig. 3) to zero at the peak of the senescent 

 deaths. In effect it is assumed in Fig. 3 that no deaths before 



