In general insurance, claims are often lower-truncated and right-censored because insurance contracts may involve deductibles and maximal covers. Most classical statistical models are not (directly) suited to model lower-truncated and right-censored claims. A surprisingly flexible family of distributions that can cope with lower-truncated and right-censored claims is the class of MBBEFD distributions that originally has been introduced by Bernegger (1997) for reinsurance pricing, but which has not gained much attention outside the reinsurance literature. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class. We show that this class contains both types of densities, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. In addition, we discuss how changes in the deductible or the maximal cover affect the chosen distributions.

翻译：在一般保险业务中，由于保单通常涉及免赔额和最高赔付限额，索赔数据常呈现低截断与右删失特征。大多数经典统计模型并不（直接）适用于此类低截断与右删失索赔的建模。MBBEFD分布族是一个能够处理这类数据的灵活分布族，最初由Bernegger（1997）提出用于再保险定价，但该分布族在再保险文献之外并未获得广泛关注。值得关注的是，一般保险领域主要依赖单峰偏态密度，而再保险文献通常建议在MBBEFD类中使用单调递减密度。研究表明该分布族同时包含这两种密度类型，我们将其扩展为更适用于低截断与右删失索赔建模的分布函数族。此外，本文还探讨了免赔额或最高赔付限额变化对所选分布的影响机制。