PERBANDINGAN HUKUM MORTALITAS GOMPERTZ DAN MAKEHAM DALAM KONSTRUKSI TABEL MORTALITAS INDONESIA IV

Abstract

Developing accurate mortality tables that reflect real conditions is a major challenge. Some researchers have proposed mortality laws using relatively simple equations that consider only age. Gompertz’s law accounts for the increasing risk of death with age, while Makeham’s law adds age-independent risk factors. This study aims to estimate the parameters of the probability of death function in both Gompertz and Makeham laws using the least squares method. The estimation process involves minimizing the squared error function of the mortality probability to form a normal equation. In this study, the resulting equation cannot be solved explicitly, a numerical approach using the Secant method is applied. The estimated parameters are then used to construct a mortality odds table, which is compared with data from the Indonesian Mortality Table IV. Model evaluation using the Mean Squared Error (MSE). The results of the analysis show that the Makeham model with the least squares method provides the best performance, indicated by the lowest MSE value of 0.0002002492 for men and 0.0003069904 for women. These findings indicate that the Makeham model outperforms the Gompertz model in constructing mortality tables using the least squares method.