The Claim Counts Model Based On The Correctional Negative Binomial Distribution

In the actual research of natural and social sciences, there is a special kind of count data. Observe events contain a lot of zero which called zero-inflation. At this point, because of the high proportion of zero incident, Beyond the traditional models’ predictive ability. Under the circumstances, applying traditional claim counts model such as poisson model, negative binomial model will lead to the deviation of parameter estimation results and the real value is too large, and they can’t accurately predict losses. On this occasion, Johnson and Kotz(1969)put forward the zero-inflated model. Based on this model, Mullay(1986) put forward another model which called Hurdle model to solve the zero-inflation. These two kinds of models provide a good research idea to solve the zero-inflation.Because of risk of non homogenous can described by negative binomial distribution very well, let it widely used in the risk management. Probit function is also widely used in various fields because of its normality. In this paper, PNB-Hurdle model, ZINB model and PC-ZINB model which correct structural zero are established based on the negative binomial distribution and link function which is Probit function, and testing these models with stochastic simulation method. The results show that when the three models fit the zero-inflation count data, their imitative effects are better than traditional count data model.With the vigorous development of Chinese economy, the insurance industry in China’s growth is accelerating. Especially the car insurance, which has become the largest share of ownership in non-life insurance. Nowadays, the development of the car insurance concerns to the survival of non-life insurance companies. Therefore, the study of car insurance is very meaningful. In this background, this paper combines the actual claims data of car insurance, using the poisson model, negative binomial model, PNB-Hurdle model, GLNB model, ZINB model and PC-ZINB model to doing parameter estimation and claims data prediction. The results show that, because of the non homogeneity of the data, the classic poisson model loses its simulation effect. Although the traditional negative binomial model can solve the problem of non homogeneity, the existence of the phenomenon of zero-inflation leads to the simulation effect is not very good. In the same way, although the generalized negative binomial model can explain the influencing factors, the existence of the phenomenon of zero-inflation leads to the fitting effect is not very good too. While PNB-Hurdle model is possible to solve the problem of zero-inflation, but for this empirical data, its advantages have not been shown. Conversely, zero-inflated models have shown the good simulation effect in the empirical research. Especially the PC-ZINB model, it perfectly correct the probability of zero and solve the problem of zero-inflation very well.As a consequence, for the zero-inflated data: If the source of zero is relatively single, the simple PNB-Hurdle model can be simulated well. If the source of structural zero is relatively single, the ZINB model can have a good simulation effect. If the source of structural zero is very complex and contains influence factors of different nature, the PC-ZINB model will be more suitable for prediction the data. And for the zero-inflated model, making the structural zero divided into the objective structure and subjective structure is feasible, especially in car insurance.