Insurance loss distributions are characterized by a high frequency of small claim amounts and a lower, but not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the ‘body’ and the other for the ‘tail’ of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fit and compare the competing models. The method is validated via a simulation study and illustrated on an insurance loss dataset.

保险损失分布的特点是小额索赔发生的频率较高，而大额索赔发生的频率较低，但并非微不足道。精算文献中出现了将两种概率分布（一种用于损失分布的“主体”，另一种用于“尾部”）联系起来的复合模型，以考虑到这种特殊性。这些模型的参数总结了损失的分布。其中之一对应于小额索赔金额和大额索赔金额之间的分界点。复合模型通常使用最大似然估计来拟合。这项工作考虑了贝叶斯方法。顺序蒙特卡洛采样器用于从后验分布中采样并计算后验模型证据以拟合和比较竞争模型。