Statistical Model Of Water-related Insurance Claims

This paper mainly studies the statistical model of Water-related(rainfall and snow melting)insurance claims under the condition of claim occurrence.Firstly,the Bayesian Poisson hurdle model,Zero-truncated Poisson distribution model,Mixture zero-truncated Poisson distribution model and the Mixture extreme model based on the integer-valued Generalized Pareto distribution and Zero-truncated Poisson distribution are proposed.Then,we introduce a tail optimization method to deal with weather covariates which can better reflect the dependence between large claims and extreme weather.Furthermore,clustering approach which can be considered the interaction between continuous time precipitation and insurance claims is introduced as well.By this way,the cluster data can be obtained.Finally,the data obtained by clustering approach are used to test the Zero-truncated Poisson distribution model,the Mixture zero-truncated Poisson distribution model and the Mixture extreme model respectively.The results show that the first two models can not pass the test,but the Mixture extreme model can pass the test,so it can better reflect the probability distribution of insurance claims under extreme weather conditions.