Generalized Linear Model Besed On Bell Distribution Class And Its Application To Auto Insurance Claim Number Fitting

In a series of auto insurance reforms,the state has continuously relaxed its intervention in the auto insurance market,attached importance of and highlighted the initiative of property insurance companies,and obtained a more reasonable auto insurance rate standard,which is more and more important to the development of property insurance companies and the market.The number of auto insurance claims is intended to be an important part of the determination of auto insurance rate.The quality of fitting effect will directly affect the accuracy of the rate.Therefore,the primary solution to obtain a reasonable rate standard should be the fitting of the number of auto insurance claim.In this case,the traditional hypothesis distribution is still used for data fitting,which often cannot accurately describe the data characteristics,resulting in poor model fitting effect.However,Bell distribution mainly includes Bell distribution and Bell-Touchard distribution(BT distribution).These two distributions not only have simple expressions,but also have the distribution characteristics of over discrete and zero expansion,which is more reasonable for the fitting of the actual number of auto insurance claims data.Therefore,this thesis introduces the Bell distribution class of the generalized linear model for the first time,constructs the Bell regression model and BT regression model,and applies the Bell regression model on the auto insurance claim number fitting,so as to solve the problem that the traditional hypothesis distribution can not well describe the characteristics of over-discretization and zero expansion in the actual auto insurance claim number data.The main contents of this thesis are as follows :(1)the parameter estimation method of Bell distribution and BT distribution are given,so as to promote the application of BT distribution of the field of finance and insurance.(2)The Bell distribution class is introduced into the generalized linear model,and the Bell regression model and BT regression model are established respectively.At the same time,the parameter estimation and model testing methods of the two models are given.(3)An empirical analysis of the model was carried out based on a group of actual auto insurance claim number data onto Australia,and the selection of model variables and the processing method of auto insurance claims number data was discussed.At the same time,a regression model was established according to the eight hypothesis distributions introduced,and the fitting effects of each model were analyzed and compared.The results show that :(1)there is obvious over-discrete characteristics in the actual number of auto insurance claims data,and the regression models on over-discrete distribution characteristics can obtain better fitting effect.(2)Compared with poisson’s regression model,Bell’s regression model has more advantages because of its over-discrete nature in the data modeling of auto insurance claims.(3)BT distribution is characterized by over-discretization and zero expansion,so the fitting effect of BT regression model is significantly improved when fitting the actual number of auto insurance claims,and it is better than the negative binomial model,Poisson inverse Gaussian model and zero expansion model.In conclusion,Bell regression model and BT regression model are important supplements to the traditional generalized linear model and have significant advantages in the fitting of actual counting data.At the same time,the Bell regression model and BT regression model is applied to the fitting of auto insurance claim times,which can solve the problem that the model complexity is inconsistent with the actual data of auto insurance claim times with the characteristics of over discrete and zero expansion,and provide an effective analysis method for auto insurance premium rate determination.