Comparison of Estimation Methods for the Weibull Distribution in Indonesian Life Tables

Abstract

This study evaluates the performance of the Ordinary Least Squares, Nonlinear Least Squares, and Maximum Likelihood Estimation methods in fitting the two parameter Weibull distribution to the 2019 Indonesian Life Table and the 2023 Indonesian Population Life Table, focusing on ages 59-111. The lower age bound is selected to isolate the adult and late-life mortality in which the Weibull model’s assumptions are most applicable. Although both life tables exhibit monotonically increasing mortality with the same terminal age, they differ in the age at which mortality acceleration becomes pronounced. Goodness-of-fit was assessed through a comparison of root mean squared errors, root mean squared logarithmic errors, and residual plots. The results indicate that the Ordinary Least Squares method, while computationally stable, tends to overestimate survival beyond the terminal age. The Nonlinear Least Squares method better aligns with the empirical survival yet similarly extends the terminal age. The Maximum Likelihood Estimation method provides more realistic terminal ages but inflates survival at infancy and midlife stages. These findings highlight that estimation methods and data segment selection strongly influence the reliability of Weibull-derived life tables. Applications in actuarial and demographic practices require improved estimation strategies to better capture late-age mortality.