Fitting of Finite Mixture Distributions to Motor Insurance Claims

Problem statement: The modeling of claims is an important task of actuaries. Our problem is in modelling the actual motor insurance claim data set. In this study, we show that the actual motor insurance claim can be fitted by a finite mixture model. Approach: Firstly, we analyse the actual data set and then we choose the finite mixture Lognormal distributions as our model. The estimated parameters of the model are obtained from the EM algorithm. Then, we use the K-S and A-D test for showing how well the finite mixture Lognormal distributions fit the actual data set. We also mention the bootstrap technique in estimating the parameters. Results: From the tests, we found that the finite mixture lognormal distributions fit the actual data set with significant level 0.10. Conclusion: The finite mixture Lognormal distributions can be fitted to motor insurance claims and this fitting is better when the number of components (k) are increase.