We consider the situation when the number of claims is unavailable, and a Tweedie's compound Poisson model is fitted to the observed pure premium. Currently, there are two different models based on the Tweedie distribution: a single generalized linear model (GLM) for mean and a double generalized linear model (DGLM) for both mean and dispersion. Although the DGLM approach facilitates the heterogeneous dispersion, its soundness relies on the accuracy of the saddlepoint approximation, which is poor when the proportion of zero claims is large. For both models, the power variance parameter is estimated by considering the profile likelihood, which is computationally expensive. We propose a new approach to fit the Tweedie model with the EM algorithm, which is equivalent to an iteratively re-weighted Poisson-gamma model on an augmented data set. The proposed approach addresses the heterogeneous dispersion without needing the saddlepoint approximation, and the power variance parameter is estimated during the model fitting. Numerical examples show that our proposed approach is superior to the two competing models.

我们考虑当索赔数量不可用时的情况，并且将 Tweedie 复合泊松模型拟合到观察到的纯保费。目前，有两种基于 Tweedie 分布的不同模型：均值的单广义线性模型(GLM) 和均值和离散度的双广义线性模型 (DGLM)。尽管DGLM方法有利于异质分散，但其稳健性依赖于鞍点近似的准确性，当零索赔比例较大时，鞍点近似的准确性较差。对于这两种模型，功率方差参数是通过考虑轮廓似然来估计的，这在计算上是昂贵的。我们提出了一种用 EM 算法拟合 Tweedie 模型的新方法，这相当于在增强数据集上迭代重新加权的 Poisson-gamma 模型。该方法无需鞍点近似即可解决异质色散问题，并且在模型拟合期间估计功率方差参数。数值例子表明我们提出的方法优于两个竞争模型。