ABSTRACT A correct modelization of the insurance losses distribution is crucial in the insurance industry. This distribution is generally highly positively skewed, unimodal hump-shaped, and with a heavy right tail. Compound models are a profitable way to accommodate situations in which some of the probability masses are shifted to the tails of the distribution. Therefore, in this work, a general approach to compound unimodal hump-shaped distributions with a mixing dichotomous distribution is introduced. A 2-parameter unimodal hump-shaped distribution, defined on a positive support, is considered and reparametrized with respect to the mode and to another parameter related to the distribution variability. The compound is performed by scaling the latter parameter by means of a dichotomous mixing distribution that governs the tail behavior of the resulting model. The proposed model can also allow for automatic detection of typical and atypical losses via a simple procedure based on maximum a posteriori probabilities. Unimodal gamma and log-normal are considered as examples of unimodal hump-shaped distributions. The resulting models are firstly evaluated in a sensitivity study and then fitted to two real insurance loss datasets, along with several well-known competitors. Likelihood-based information criteria and risk measures are used to compare the models.

中文翻译：

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二分单峰复合模型：在保险损失分配中的应用

摘要 保险损失分布的正确模型化在保险业中至关重要。这种分布通常是高度正偏斜的，单峰驼峰形，右尾很重。复合模型是适应某些概率质量转移到分布尾部的情况的一种有利可图的方式。因此，在这项工作中，介绍了一种具有混合二分分布的复合单峰驼峰分布的一般方法。在正支撑上定义的 2 参数单峰驼峰形分布被考虑并根据模式和与分布变异性相关的另一个参数重新参数化。该复合是通过使用控制所得模型的尾部行为的二分混合分布来缩放后一个参数来执行的。所提出的模型还可以通过基于最大后验概率的简单程序自动检测典型和非典型损失。单峰伽马和对数正态被认为是单峰驼峰形分布的示例。生成的模型首先在敏感性研究中进行评估，然后与几个著名的竞争对手一起拟合到两个真实的保险损失数据集。基于可能性的信息标准和风险度量用于比较模型。单峰伽马和对数正态被认为是单峰驼峰形分布的示例。生成的模型首先在敏感性研究中进行评估，然后与几个著名的竞争对手一起拟合到两个真实的保险损失数据集。基于可能性的信息标准和风险度量用于比较模型。单峰伽马和对数正态被认为是单峰驼峰形分布的示例。生成的模型首先在敏感性研究中进行评估，然后与几个著名的竞争对手一起拟合到两个真实的保险损失数据集。基于可能性的信息标准和风险度量用于比较模型。