Modeling Third-Party Liability Claim Frequency Data Using Mixture Poisson Distribution Through the Parametric Bootstrap Approach
Hudan Wahyudin, Aceng Komarudin Mutaqin, Sutawanir Darwis

Department of Statistics, Universitas Islam Bandung

Abstract

One type of protection in automobile insurance is the third-party liability coverage. The benefits of the third-party liability coverage include protection against the risk of death or injury to a third party and damage to property or assets of the third party. One of the important variables in determining premiums for the third-party liability coverage is claim frequency data. A commonly used statistical model for claims frequency data is the Poisson distribution. In practice, claims frequency data often exhibits overdispersion, meaning the variance in the claim frequency data exceeds its mean. To address this problem, the mixture Poisson distribution is often used. This distribution is a mixture of the Poisson distribution and the distribution of Poisson parameter. In constructing a Poisson mixture distribution, the distribution of Poisson parameters is determined without any data. In this study, the distribution of Poisson parameter is based on claim frequency data of the third-party liability coverage using a parametric bootstrap approach. The maximum likelihood estimation method is used to estimate the parameters of the mixture Poisson distribution. The chi-square test is used to test the goodness-of-fit of the mixture Poisson distribution. The method proposed in this study will be applied to the claim frequency data of the third-party liability coverage on truck type vehicles in Indonesia in the underwriting year 2018. The results of the study indicate that the mixture Poisson distribution fits the above data. The estimated mean is 0.0214, and the estimated variance is 0.0228.

Keywords: mixture Poisson- maximum likelihood estimation- parametric bootstrap approach- chi-square test- third-party liability coverage

Topic: Mathematics