Standard count models such as the Poisson and Negative Binomial models often fail to capture the large proportion of zero claims commonly observed in insurance data. To address such issue of excessive zeros, zero-inflated and hurdle models introduce additional parameters that explicitly account for excess zeros, thereby improving the joint representation of zero and positive claim outcomes. These models have further been extended with random effects to accommodate longitudinal dependence and unobserved heterogeneity. However, their consistency with fundamental probabilistic principles in insurance, particularly stochastic monotonicity, has not been formally examined. This paper provides a rigorous analysis showing that standard counting random-effect models for excessive zeros may violate this property, leading to inconsistencies in posterior credibility. We then propose new classes of counting random-effect models that both accommodate excessive zeros and ensure stochastic monotonicity, thereby providing fair and theoretically coherent credibility adjustments as claim histories evolve.

翻译：标准的计数模型（如泊松模型和负二项模型）往往难以捕捉保险数据中常见的零索赔高比例现象。为解决此类过度零值问题，零膨胀模型和跨栏模型通过引入额外参数来显式处理超额零值，从而改善对零索赔与正索赔结果的联合表征。这些模型进一步通过引入随机效应进行扩展，以处理纵向依赖性和未观测异质性。然而，这些模型与保险领域基本概率原理（特别是随机单调性）的一致性尚未得到严格检验。本文通过严谨分析表明，标准的过度零值随机效应计数模型可能违反该性质，导致后验信度估计不一致。我们进而提出新的随机效应计数模型族，既能处理过度零值问题，又能保证随机单调性，从而在索赔历史演变过程中提供公平且理论一致的信度调整。