Statistical Analysis Of Zero Inflated Tweedie Compound Poisson Gamma Model

In the study of determing auto insurance premium rates,estimating net premium(expected claim cost)is the focus of the study.Total auto insurance claims are typically modeled with a Tweedie compound Poisson gamma model.However,when the proportion of zero claims is too large and the distribution of total claims amounts is extremely unbalanced,the Tweedie compound Poisson gamma model also cannot capture the excessive zero characteristic of the data.To this end,we propose a zero-inflated Tweedie compound Poisson gamma distribution and a corresponding zero-inflated Tweedie compound Poisson gamma parametric regression model to address the above problems.In this paper,we mainly conduct statistical analysis on the zero-inflated Tweedie compound Poisson gamma model(distribution and corresponding regression model).Firstly,the form of model is given,then maximum likelihood estimation and Bayesian estimation of parameters in the model are discussed in detail.In order to reduce the difficulty of optimization,we introduce latent variables and use the EM algorithm to give the maximum likelihood estimation of the parameters.Based on a latent variable,a hybrid algorithm of the MH algorithm and the Gibbs sampling,is used to obtain random samples of the posterior distribution of the parameters,and further obtain the Bayesian estimation of the parameters.Secondly,numerical simulations are carried out which is aimed for verifing the correctness of the proposed model and the effectiveness of the parameter estimation methods.Finally,the validity of the proposed model is verified by the actual case analysis of auto insurance data.The experimental results show that the zero-inflated Tweedie compound Poisson gamma model is better than the Tweedie compound Poisson gamma model on extremely unbalanced data with an excessively large proportion of zero claims,which also verifies the effectiveness of the maximum likelihood estimation based on the EM algorithm and a Bayesian estimation based on Gibbs sampling.