Insurance loss severity data often exhibit heavy-tailed behavior, complex distributional characteristics such as multimodality, and peculiar links between policyholders’ risk profiles and claim amounts. To capture these features, we propose a transformed Gamma logit-weighted mixture of experts (TG-LRMoE) model for severity regression. The model possesses several desirable properties. The TG-LRMoE satisfies the denseness property that warrants its full versatility in capturing any distribution and regression structures. It may effectively extrapolate a wide range of tail behavior. The model is also identifiable, which further ensures its suitability for statistical inference. To make the TG-LRMoE computationally tractable, an expectation conditional maximization (ECM) algorithm with parameter penalization is developed for efficient and robust parameter estimation. The proposed model is applied to fit the severity and reporting delay components of a European automobile insurance dataset. In addition to obtaining excellent goodness of fit, the proposed model is shown to be useful and crucial for adequate prediction of incurred but not reported (IBNR) reserves through out-of-sample testing.

保险损失严重程度数据通常表现出重尾行为、复杂的分布特征（例如多模态）以及保单持有人的风险状况与索赔金额之间的特殊联系。为了捕捉这些特征，我们提出了一个经过转换的 Gamma 对数加权专家混合（TG-LRMoE）模型，用于严重性回归。该模型具有几个理想的特性。TG-LRMoE 满足密度特性，保证其在捕获任何分布和回归结构方面的全面性。它可以有效地推断出广泛的尾部行为。该模型也是可识别的，这进一步确保了其适用于统计推断。为了使 TG-LRMoE 在计算上易于处理，开发了一种具有参数惩罚的期望条件最大化 (ECM) 算法，用于有效和稳健的参数估计。所提出的模型用于拟合欧洲汽车保险数据集的严重性和报告延迟组件。除了获得出色的拟合优度外，所提出的模型对于通过样本外测试充分预测已发生但未报告 (IBNR) 储量是有用和关键的。