The B\"uhlmann model, a branch of classical credibility theory, has been successively applied to the premium estimation for group insurance contracts and other insurance specifications. In this paper, we develop a robust B\"uhlmann credibility via the censored version of loss data, or the censored mean (a robust alternative to traditional individual mean). This framework yields explicit formulas of structural parameters in credibility estimation for both scale-shape distribution families, location-scale distribution families, and their variants, which are commonly used to model insurance risks. The asymptotic properties of the proposed method are provided and corroborated through simulations, and their performance is compared to that of credibility based on the trimmed mean. By varying the censoring/trimming threshold level in several parametric models, we find all structural parameters via censoring are less volatile compared to the corresponding quantities via trimming, and using censored mean as a robust risk measure will reduce the influence of parametric loss assumptions on credibility estimation. Besides, the non-parametric estimations in credibility are discussed using the theory of $L-$estimators. And a numerical illustration from Wisconsin Local Government Property Insurance Fund indicates that the proposed robust credibility can prevent the effect caused by model mis-specification and capture the risk behavior of loss data in a broader viewpoint.

翻译：经典可信度理论分支中的Bühlmann模型已成功应用于团体保险合同及其他保险场景的保费估计。本文通过损失数据的截断版本（即截断均值，作为传统个体均值的稳健替代）构建了稳健的Bühlmann可信度模型。该框架为保险风险建模中常用的尺度-形状分布族、位置-尺度分布族及其变体提供了可信度估计中结构参数的显式公式。我们给出了所提方法的渐近性质并通过模拟验证，同时将其性能与基于修剪均值的可信度方法进行了比较。通过在不同参数模型中调整截断/修剪阈值水平，我们发现基于截断方法的所有结构参数波动性均小于对应的修剪方法，且采用截断均值作为稳健风险测度可降低参数损失假设对可信度估计的影响。此外，本文利用L-估计量理论讨论了可信度中的非参数估计方法。威斯康星州地方政府财产保险基金的数值实例表明，所提出的稳健可信度方法能够防范模型误设带来的影响，并从更广阔的视角捕捉损失数据的风险行为。