过离散次数分布模型的尾部特征

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.当实际数据的尾部较长(即过离散),且零点的概率较大时,许多模型的拟合效果往往欠佳.本文通过计算概率之比的极限和偏度系数,对混合泊松分布和复合泊松分布的右尾特征和零点概率进行了比较,给出了它们的尾部排列顺序,以及尾部长短与零点概率的关系,从而为模型的构造或选择提供了一种指导.本文最后应用一组实际数据说明了在构造或选择次数分布模型时如何考虑尾部特征,从而改善对实际数据的拟合效果.

Tail Behavior of Over-Dispersed Counts Distributions

Discrete counts models are widely used in actuarial science and biometrical statistics.Many models are not suitable for fitting the actual data when the data has a long tail(i.e.over-dispersed)and has a large probability at zero.Using the limiting probability ratios and the skewness,the paper compares the mixed Poisson distributions and the compound Poisson distributions,ranks these distributions by their right tails and the probabilities at zero,and then provides a direction for constructing or selecting models.At the end,the paper applies the models to a real data set to explain how to consider its tail behavior when constructing or selecting a model to fit the data.