Expanding an Abridged Life Table Using the Heligman-Pollard Model

Abstract

An estimation procedure for calculating the one-year probabilities of dying from five year ones given in an abridged life table will be proposed in the study. The expansion technique used in the study is the Heligman-Pollard model. The evaluation of this technique and several other techniques for expanding an abridged life table will be explained in this paper. Since the model involves nonlinear equations that are explicitly difficult to solve, the Matrix Laboratory Version 7.0 (MATLAB 7.0) software will be used in the study. A nonlinear least squares algorithm with the capability of approximating numerically all derivatives was used in order to estimate the parameters of the model. This algorithm is based upon a modification of the Gauss Newton iteration procedure, known as Levenberg-Marquardt iteration procedure. The empirical data sets of Malaysia population for the period of 1991-2000 and for both genders will be considered. Keywords: Abridged life table; Heligman-Pollard model; Modification of the Gauss Newton iteration; Levenberg-Marquardt iteration.