中文摘要：

在保险精算和生物统计等领域,离散型次数分布模型的应用十分广泛,仅用常用的分布类模拟实际数据拟合效果往往欠佳。首先给出了分布类概率分布的证明,讨论了计算分布点估计法;然后证明了分布类概率生成函数的一般表达式,应用概率生成函数,得出了计算复合泊松分布概率分布的Panjer递推公式;最后应用一组实际数据说明了如何选择模型,应用Panjer递推算法在Matlab环境下实现了复合分布的点估计,拟合分布结果表明,复合泊松分布的拟合效果较好,改善了对实际数据的拟合效果,从而为模型的构造和选择提供了理论依据和方法。

英文摘要：

Discrete counts models are widely used in acturary and biostatistics,but just use the distribution class,（a,b,0）,is not suitable for fitting the actual data.This test firstly gave the proof of the（a,b,1） distribution class＇s distribution and also discussed the point estimate method to calculate the distribution point of（a,b,1）.Then it proved the general expression of the probability of（a,b,1） distribution class generated function.We applied probability for generating function to get the Panjer Recursive Algorithm which is used to calculate compound Poisson distribution＇s probability distribution.Finally,the paper app-lied a set of data to explain how to choose models.The application of Panjer Recursive Algorithm accomplished the point estimate of the compound distribution in the environment of Mtlam.The fitting distribution results showed that the compound Pisson distribution do better in fitting.It improved the fitting results of actual data,thus provided a theoretical basis and method of constructing and selecting models.