A simple equation for estimating the expectation of life at old ages

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Abstract
There is much direct and indirect evidence that in a number of populations the ages of older persons tend to be exaggerated, both when reported in censuses and in records of deaths. This results in overestimated expectations of life at old ages. The bias may be corrected by estimating the expectation of life at age a, e(a), from the mortality rate and growth rate at age a and above, M(a+) and r(a+), using the equation developed in this paper: 1/ê(a) = M(a+) exp (β . r(a+). M(a+)−α). For a ⩾, 65, α = 1.4 and β = 0.0951 have been chosen. The value of the equation rests on the following: since ages of older persons tend to be exaggerated, there may be an age a such that most age transfer occurs above that age, and age transfer across the age is small or cancels, so that reasonably accurate values of M(a+) and r(a +) can be obtained, even though ages are badly reported above a. The analysis of artificial data on Gompertzian stable popultions aged over 50 and actual statistics for some selected populations has suggested that the equation provides quite accurate estimates of e(a). The equation also seems useful in closing life tables, since it provides a value of e(a) for the highest age group

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