PEMODELAN KREDIBILITAS BÜHLMANN-STRAUB UNTUK DATA FREKUENSI KLAIM BERDISTRIBUSI POISSON-SUJATHA

Abstract

Motor vehicle insurance provides compensation for damage or loss incurred by motor vehicles. In determining credibility values, claim frequency data is required. Sometimes, this claim frequency data contains overdispersion issues, necessitating alternative methods for modeling claim frequency using a mixture distribution. The mixture distribution used in this research is the Poisson-Sujatha mixture distribution. The credibility method employed is an advancement of the Bühlmann method, known as the Bühlmann-Straub credibility method. The BühlmannStraub credibility model has been successfully applied in various insurance contexts, previously used in modeling with the Negative Binomial-Lindley distribution in 2023, yielding significant results. Before applying the credibility model, the parameters of the PoissonSujatha distribution are estimated using the maximum likelihood estimation method. The goodness-of-fit test used in this research is the chi-squared goodness-of-fit test. The research data consists of secondary claim frequency data for motor vehicle insurance recorded by PT. X in Category 1 (passenger transport with coverage values between Rp 0 to Rp 125,000,000) in Region 2 (DKI Jakarta, West Java, and Banten) for 2018 and 2019. Based on the application of this claim frequency data, the Bühlmann-Straub credibility factor is close to 1, indicating that the processed data has a significant impact on estimating the average future claim frequency. The estimated average motor insurance claim frequency for Indonesia, Category 1, Region 2, in 2020 is 0.0041, meaning that if there are 10,000 insurance policyholders in 2020, approximately 41 partial loss claims are expected.