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. We derive properties of the class of MBBEFD distributions, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class.

翻译：在一般保险中，由于保险合同可能涉及免赔额和最高保额，索赔数据通常存在下限截断和右删失特征。多数经典统计模型并不（直接）适用于此类数据的建模。能够有效处理下限截断和右删失索赔的是一类被称为MBBEFD分布的灵活分布族，该分布最初由Bernegger（1997）提出用于再保险定价，但在再保险文献之外并未获得广泛关注。本文推导了MBBEFD分布族的性质，并将其扩展为适用于下限截断和右删失索赔建模的更广泛分布函数族。值得注意的是，一般保险领域主要依赖单峰偏态密度函数，而再保险文献中通常建议采用MBBEFD类中的单调递减密度函数。