A General Theory of Life Table Construction and a Precise Abridged Life Table Method

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Abstract
In this paper we lay the foundation of life table construction by unifying the existing life table methods. We also present a new method of constructing current (period) abridged life tables. The proposed method produces more life talbe functions than other existing methods do. The development includes (1) a careful formulation and computation of age‐specific death rates, (2) derivation of a new set of formulas for computing the survivorship function from the observed age‐specific death rates and populations, (3) estimation of the main life table functions by spline interpolation, integration and differentiation, and (4) use of a quadratic and a Gompertz function to close the life table. The new abridged life table method features (i) improved accuracy, (ii) tolerance to observed age distributions with bulges and dents and (iii), together with the infant life table method of HSIEH (1985), coverage of the whole life span. The method is illustrated with construction of abridged life tables using Canadian data.