Statistical Analysis Of Auto-Mobile Insurance Claim Data Based On Copula Model

Auto-mobile insurance is vital in the field of non-life insurance. Based on the study of auto-mobile insurance claims, insurance company could make more suit-able insurance contracts with reasonable prices. To analyze the insurance data, the dependency among them, like the relationship within time longitudinal auto-mobile insurance claim counts or the relationship between insurance claim counts and aver-age claim amount, should be concentrated. If that dependency could be described by a multivariate model, it will be very helpful for the related study.The aims of this paper are to study the dependency among auto-mobile insurance claim counts and the claim amounts, and the relationship within time longitudinal in-surance claim counts. We firstly discuss the Copula model with groups of marginal re-gressions, like that of inverse Gaussian and negative binomial regression model. Then we estimate the related parameters, by the help of Inference function for margins ( IFM) estimation method. Secondly, the maximum likelihood estimates of mixture Copula model are studied by combining IFM and EM methods. At last, we apply the Copula model to the time longitudinal data. We take advantage of one order markov model and jitter approach to build several combination models and to simplify the re-lated estimation. In addition, to examine the validity of the adopted methods, through the Monte Carlo simulation method, we generate data sets with different amounts and different sizes, and obtain the estimates. Meanwhile, we apply the copula models constructed in this paper to the insurance claim data and obtain the consequences that correspond to the common-sense.