Estimation of Gompertz Mortality Parameter Models on Indonesian Population Mortality Table 2023

Abstract

The research article discuss Gompertz Mortality Law parameter estimation using several methods to get the best models. The data based from Indonesian population mortality table or called Tabel Mortalitas Penduduk Indonesia (TMPI) 2023. Parameter estimation using several methods, includes Nonlinear Least Square (NLLS) with the Gauss-Newton algorithm, Weighted Least Squares (WLS), and Poisson Regression. Model validation is done by calculating root mean square error (RMSE) to determine the most accurate method. The analysis includes calculation of values in the mortality table, transformation of the gompertz model, estimated parameters with each method, and RMSE calculation. In the WLS method, the estimation is carried out by transformation of natural logarithms from the force of mortality function, then minimizes the number of squares of error, with 𝑑𝑥 as weight and forming the 𝑑𝑥 function and maximizing the logordered function on Poisson regression. Model accuracy is assessed from the suitability between the 𝑞𝑥 function value of the model results with the 𝑞𝑥 value in TMPI, both visually and mathematically through RMSE. The analysis results show that the NLLS method with the Gauss-Newton algorithm produces the most accurate Gompertz model.