Abstract

We propose a family of distributions as an alternative for a recent compound unimodal distribution for modeling insurance losses. The family of distributions, referred to as density-hazard distributions, has closed form density and distribution functions, hence easier to fit and simulate from. The distributions also show good adherence to insurance loss data and estimates risk measures relatively closely to the empirical values. In this respect, the practical use of the density-hazard distributions is demonstrated with the employment of three real insurance data including the U.S. indemnity insurance loss data, the U.S. automobile claims data, and the Norwegian fire losses data.

摘要

我们提出了一系列分布作为最近用于模拟保险损失的复合单峰分布的替代方案。分布族，称为密度危险分布，具有封闭形式的密度和分布函数，因此更易于拟合和模拟。这些分布还显示出对保险损失数据的良好遵守，并且估计风险度量与经验值相对接近。在这方面，通过使用三个真实的保险数据，包括美国赔偿保险损失数据、美国汽车索赔数据和挪威火灾损失数据，证明了密度-危险分布的实际应用。