Abridged Adult Mortality Table from Cumulative Life Table Survival Ratios – T(x+5)/T(x) above Age 5: Two New Approaches

This study presents two approaches of constructing adult mortality table or life table from an appropriate set of survival probability (p-values) from a given set of 5-year cumulative life table survival ratios (in short, 5-cum-LSRs), defined by the ratios T(x+5)/T(x), beyond age 5. The set of survival probability (p-values) over ages, so obtained, is not only consistent with the given set of 5-cum-LSRs but also satisfy the usual properties and depicts the true trends of life table p-values over ages. The two approaches for estimating survival probabilities at various quinquennial ages are as follows -- one makes use of algebraic chain relationships between two survival probabilities in the adjacent 5-year age-intervals for a given set of 5-cum-LSRs, and the other one is based on an iterative procedure under conventional and Greville’s approximations for estimating L(x, x+5) from l(x). The empirical investigations of the two approaches based on model life tables show that the estimated p-values and hence the mortality table so obtained beyond age 5 are almost identical to the true one under certain condition. The empirical and analytical investigations show that non-conventional method (that of Greville's) converges much faster than the conventional method of life table construction. Convergence can be proved mathematically .