Distribution Models of Claim Frequency and Claim Severity in Determining the Pure Premium of Car Insurance with the Application of a Deductible

Manurung, Tohap (Universitas Sam Ratulangi)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan

The objective of this study is to determine the pure premium value based on a car damage claim data model from car insurance company X, using data that applies a deductible value. The data used comprises car damage claims with deductibles applied during a year period. Determining the distribution model for insurance claims is one of the relevant techniques for measuring operational risk in insurance companies. In this context, historical claim data is tested against existing distribution models, enabling the calculation of pure premium values for the insurance company. The results show that the claim frequency data follows a Negative Binomial distribution with an expected value of E(N) = 0.0107, and the claim severity data follows a Log-logistic distribution with E(X) = 12,037,950. Therefore, the calculated pure premium value is E(S) = Rp129,205.19. The pure premium obtained serves as the basis for determining the actual premium charged to policyholders, with the addition of loadings.