Comparison of Pure Premiums for Motor Vehicle Insurance Using ZTP-Gamma GLM and Tweedie GLM

Yushinta Cahya Lestari (Department of Actuarial Science, Sumatera Institute of Technology, Lampung, 35365, Indonesia)
Tiara Yulita (Department of Actuarial Science, Sumatera Institute of Technology, Lampung, 35365, Indonesia)
Amalia Listiani (Department of Actuarial Science, Sumatera Institute of Technology, Lampung, 35365, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan

The increasing number of motor vehicles has contributed to higher traffic density and a greater risk of accidents, thereby reinforcing the importance of protection through motor vehicle insurance. Therefore, accurately determining the pure premium is essential to maintain risk balance and ensure the sustainability of insurance companies. This study employs Generalized Linear Models, which are an extension of classical linear regression that allow the response variable to follow non-normal distributions, particularly the Zero-Truncated Poisson, Gamma, and Tweedie distributions. Using motor vehicle insurance claim data from 2022 with 386 observations, this research compares two premium modeling approaches, namely the ZTP–Gamma model for estimating claim frequency and claim severity, and the Tweedie GLM for modeling total claims in the calculation of pure premiums for motor vehicle insurance. The analysis shows that the estimated pure premiums for the ZTP–Gamma GLM range from IDR 2,138,532 to IDR 19,939,391, while the estimates for the Tweedie GLM range from IDR 2,153,665 to IDR 20,936,047. The ZTP–Gamma GLM demonstrates better accuracy, with a MAPE value of 23.65% compared to 25.844% for the Tweedie GLM, resulting in an accuracy difference of 2.194%. These findings indicate that the ZTP–Gamma GLM is more effective in producing accurate pure premium estimates.