Generalized Linear Models, Generalized Linear Mixed Models And Their Applications

Generalized linear model(GLM) and Generalized linear mixed model(GLMM) are two classes of widely used statistical models, they have very important role in statistics theory and application fields. this article mainly discuss the two models's applications in insurance and province people death rate statistics. in insurance application, we put prior information into rate model by GLM model, result in a model contained prior information. so the rate model, which contains prior information and claim frequency and claim severity,is more scientific and accurate. in Generalized linear mixed model application,we apply the GLMM model to death rate data of xinjiang province people and analyses effects of factors on the death rate.we discuss the effect of age, sex, death year and region factors to province people death rate. we analyses the data (19333 observations) of xinjiang five town in two years, among factors, sex and age are regarded as fixed effects and death year and region are regarded as random effects.The conclusion show that the model has significance in practice.