Statistical Inference Of Tweedie Regression Model And Its Application

Recently,the Tweedie distribution has been widely used for statistical analysis in the fields of ecology,economics,environmental science,insurance,fisheries,and medicine.For example,the special case of the Tweedie distribution,the compound Poisson distribution,is often used to forecast the total claims in the insurance industry.However,there are a wide range of influential points in the data of the insurance industry,and they have a great influence on the results of statistical inference.Therefore,there is an obvious practical need to study whether the Tweedie regression model has influential points through Bayesian case influence measures.In this thesis,we studied the impact analysis of the Tweedie regression model’s data deletion under the Bayesian framework.The main work of this thesis is summarized as follows:1.Bayesian analysis of Tweedie regression models.A hybrid algorithm of Gibbs sampling and MH algorithm is used to obtain a random sample of the posterior distribution of the parameter Ψ,and further the joint Bayesian estimation of the parameters Ψ=(β,φ,p)as well as their corresponding standard deviations are obtained.2.Bayesian impact analysis of Tweedie regression model.A set of the Bayesian deletion diagnostic methods was established to evaluate the sensitivity of the model to delete influential sets.It is mainly to develop some simple and easy methods to calculate three types of Bayesian case influence measures:Φ-divergence DΦ(S),Cook posterior mean distance CM(S),Cook’s posterior mean distance CP(S).3.Simulation and case study.The first simulation examined the effectiveness of the hybrid algorithm of Gibbs sampling and MH algorithm and its sensitivity to a priori information.The second simulation used Bayesian deletion diagnostic methods to analyze the simulated data.In the case study,the maximum likelihood method and the Bayesian method were used to establish the Tweedie regression model for the claim data of car insurance,and Bayesian deletion diagnostic methods was used to obtain influential points of the actual data set.