Paper - Statistics Singapore

Estimating Mortality Rates at High Ages (Coale-Kisker method)Annex 1The Coale-Kisker method assumes a decline in the rate of increase in mortality inhigh ages, that is, m m × exp( k ) .x=x−1 xFor age x >= 85 years, definekx= kx−1− Rwherekxm= lnmxx−1Extending the formula up to age 110 yieldsk = k84= k…= k85−k86 84−k110 84−Summing the above 26 formulae, we havek84R2R26R85+ ... + k110= 26k − R(1 + ... + 26)The left hand side of the equation simplifies to ln( m110 ) − ln(m84). Solving for R,we obtain:26k84+ ln(m84) − ln(m110)R = ……… (1)351*To minimize the effects of random fluctuations, is replaced by , which isk 84k 84k*84==k82+ k83+ k845k + k83+ 3k845+ k82−853R+ k861-1