GRADUATION ANALYSIS IN MORTALITY TABLES: WHITTAKER-HENDERSON AND HELIGMAN-POLLARD - Gracsella Rusli, Jesslyn
The Mortality Table is a collection of statistical data depicting the death rates within a population, which is used in determining life insurance premiums. The data utilized to construct this Mortality Table is derived from the National Health Insurance Membership Data, spanning from January 1, 2018, to December 31, 2021. The construction process involves computing participant exposure and the number of deaths at each age, thus yielding a crude mortality rate that increases with age. Subsequently, a productive age range (15-64 years) deemed consistent is selected for extrapolation. The extrapolation results indicate that the mortality rate for male participants is inherently higher than for female participants. These results are then smoothened using the Whittaker-Henderson and Heligman-Pollard models. Although the parameters of the Heligman-Pollard model are more numerous and complex, it competes effectively with the Whittaker-Henderson model. By comparing the Residual Standard Error (RSE) values of both models, it is found that for male and female participants respectively, the RSE values using the Whittaker-Henderson Model are 0,000614 and 0,000444, while for the Heligman-Pollard Model, the RSE values for male and female participants respectively are 0,007495 and 0,006143. Therefore, the Whittaker-Henderson Model is selected for further analysis due to its lower RSE values for both genders. To assess the influence of the model mortality rate and the mortality rate on the TMI IV on future mortality rates, a credibility test is conducted. The results indicate that the credibility factor increases with age from 15 to 64 years. At an early age, credible mortality rates are more influenced by the TMI IV than the model used. However, at around 41-44 years of age, credible mortality rates are significantly influenced by both TMI IV and the model used. The peak credibility factor occurs at the age of 64, indicating that the influence of the model used is more dominant than TMI IV.