| In recent years, following the appearance of Generalized Linear Models (GLMs), there are many scholars use this tool to solve insurance problems such as set up policy rate,motility rating and reserves claiming. GLMs extend the classical linear models which have two means. firstly, regression is no longer restricted to normal data, but extend to distribution from the exponential family. This enables appropriate modelling of actuarial data. Secondly, a GLM models the effect of explanatory variables on a transformation of the mean, instead of the mean itself. Standard GLMs require a sample of independent random variables. In many actuarial problems however the assumption of independence is not filled.So when we use GLMs to solve actuarial problems wo have to ignore some important factors or use them in another way. So some scholars put the random effect into the GLMs and create the theory of Generalized Linear Mixed Models (GLMMs), GLMMs can explain the traditional actuarial theories, so the factors that was ignored or treat in other ways can be used in a correct way.The paper is organized as follows. Section 1 give an introduction of background and movitation and the actuality of the other scholars all over the world. It also gives the method of this paper. Section 2 introduce the basic concepts of GLMs,LMMs and GLMMs including parameter estimation, inferance and pridiction, then compare the three models. In section 3 we introduce the theory of traditional Credibility Theory and IBNR reserve and gives an brife introduction of the traditional method of them. In section 4 ,the paper uses the GLMM to explain the tradition Credibility models and give a GLMs method including some traditional IBNR methods .In section 5,the paper gives two data examples, one is anout the Credibility Theory and the other is about IBNR reserve. Especially in the IBNR reserve, we use the GLMs and the GLMMs to compute the data respectlively and give the differnce between the results.Finally section 6 concludes.
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