Penerapan Model Kredibilitas Bühlmann Pada Data Frekuensi Klaim Asuransi Kendaraan Bermotor Di Indonesia Yang Berdistribusi Poisson-Amarendra

Abstract

In motor vehicle insurance, policyholders are required to pay a premium to the insurance company. One method to assist insurance companies in determining premiums is credibility theory. One model from this approach is the Bühlmann credibility model. Generally, claim frequency data is overdispersed. There are various distributions suitable for addressing overdispersion, one of which is the Poisson-Amarendra distribution. The method used to estimate the parameters of the Poisson-Amarendra is the maximum likelihood method. The research material used is motor vehicle insurance data in Indonesia for the year 2019, recorded by PT. X, categorized into 8 categories and 3 regions. The results of the Chi-Square goodness-of-fit test show that the claim frequency data from the population distributed by the Poisson-Amarendra distribution includes category 2 in region 1 and category 6 in region 3. The results of applying the Bühlmann credibility model yield a credibility factor of 0.0029 for category 2 in region 1 and 0.0101 for category 6 in region 3. The estimated average claim frequency for motor vehicle insurance in the next period for category 2 in region 1 is 0.0029. This means that if the number of insurance policyholders in 2020 is the same as in 2019, which is 15,878, an estimated 46 partial loss claims will occur. The estimated average claim frequency for category 6 in region 3 is 0.0102, with an estimated 44 partial loss claims occurring in 2020, assuming the number of policyholders in 2020 remains the same as in 2019, which is 4,313.