Estimation of Gompertz, Makeham, and Weibull Distribution Model for Pension Fund Participant Data and Its Comparison with the 2019 Indonesian Mortality Table Utriweni Mukhaiyar*, Arsyad Syahroni, Alma Justica, KhaerunNisa SH, Mukhlisah
Actuarial Study Program, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, 40132, Indonesia
*Email: utriweni.mukhaiyar[at]itb.ac.id
Abstract
This study discusses the estimation of the Gompertz, Makeham, and Weibull distribution models for pension fund participant data and its comparison with the 2019 Indonesian Mortality Table. It is important for pension fund institutions to determine the most appropriate mortality assumptions for their actuarial calculations so that companies can fulfill their responsibilities in providing benefits as promised to participants at the beginning of the coverage period. In this study, researchers took data from 500 female participants and 500 male participants of the pension fund company. Based on the results of the descriptive statistics, it is known the data has negative skewness and kurtosis, which are -1.02 and -0.65 for female participants data, and -0.83 and -0.96 for male participants data. Furthermore, parameter estimation is performed on the three mortality distributions that are often used, namely the Gompertz, Makeham, and Weibull distributions using the Nonlinear Least Square (NLS) method, then the best distribution model is selected to estimate the mortality assumptions from the data of pension fund company participants. The selection of the best distribution is based on the smallest Mean Square Error (MSE) value compared to other distributions. The best distribution for female participants is the Gompertz distribution, while for male participants is the Makeham distribution. After being compared with the mortality table, the results obtained are for female participants, the most appropriate mortality assumption is using the 2019 Indonesian Mortality Table (TMI IV) because the MSE value of TMI IV is smaller than the MSE value of the Gompertz distribution. As for male participants, the mortality assumption is most appropriate using the Makeham distribution approach, because the MSE value of the Makeham distribution is smaller than the MSE value of TMI IV.
