The Application Of Negative Binomial Regression Models In Excessively Discrete Auto Insurance Data

The count data often applied to many fields, such as medicine, sociology, psychology and so on; it's an important statistical data type whose vaule of non-negative integer. The count data is analyzed using some frequently-used models, such as Poisson regression model, Negative Binomial regression model, Generalized Poisson regression model and Hurdle model. It has a special condition that conditional variance is greater than the mean, namely phenomenon of overdispersion exists in the count data. As a consequence, overdispersion data analysis has become an important statistical issues. In our daily life, vehicle insurance data contains the claim counts, claim amount,total payment and so on. The claim counts belongs to the count data, automobile insurance ratemaking is based on the analysis and model fitting of claim counts. And the Negative Binomial regression model can solute the overdispersion problem well, So this paper focus on studying the application of Negative Binomial regression model in the overdispersion vehicle insurance data.Firstly, This paper introduces mentioned models, overdispersion's definition and causing reason, possible consequences and test of overdispersion, etc. And then through an example of comparative study illustrates linear regression models are not suitable to apply for this case of when the response variable are count data.Secondly, through the empirical analysis we discussed the Poisson regression model and the negative binomial regression model to apply them for analysis the superiority of overdispersion vehicle insurance data. The results showed that, regardless of the model fitting results, the prediction effect, or practical significance of model such as negative binomial regression model is more suitable for overdispersion vehicle insurance data.Finally, the comparative study of Poisson regression models, Negative Binomial regression model and Generalized Poisson regression model for dealing with different degree of overdispersion vehicle insurance data using numerical simulation method. The results showed that for overdispersion data, the Negative Binomial regression model with the effect of changes in the degree of dispersion is always better than the Poisson regression model and Generalized Poisson regression model; when the overdispersion does not exist, the Poisson regression model and Negative Binomial regression model fitting effect is insignificant, and are superior to GeneralizedPoisson regression model. Overall, regardless of whether there is the overdispersion exists in the data, the Negative Binomial regression model is a good choice.