Evaluation and Application of the Ewbank Model

Abstract

The purpose of this paper is to evaluate the four-parameter logit model developed by Ewbank and others, to ascertain the validity and the applicability of this model, and finally to look for a more rational way of estimating the four parameters. For the past few decades, death rate has declined remarkably in both developing and developed countries. However, it is more and more difficult for either the present model life table or any other mathematical model to describe the mortality decline. It is because today's death rate is too low to be described by those models. One of the promising ways of solving this difficulty is to apply relational models. The two-parameter logit model developed by Brass is one of those relational models. But the Brass model sometimes fails to capture the mortality pattern of childhood and old ages. The Ewbank model was developed and designed to cope with this problem. It is not so popular, however, because it is rather difficult to estimate the four parameters of the model. Then, I applied the Ewbank model to Japanese life tables in order to verify the validity of the model, and tried to look for the more rational way of estimating the four parameters of the Ewbank model through various mathematical methods. As a result of the analysis, I found that the Ewbank model captures the mortality pattern of the Japanese, and that the four parameters of the model can be effectively estimated by using Simplex method and Marquardt method. As to the applicability of the Ewbank model, it might be possible to estimate the life table at any point of time from the past to the future by changing the values of the parameters of this model. I ascertained this by altering parameter α. As a result, the feasibility of this model is found to be quite high.