Abstract

Recent research in the area of univariate mixture modeling indicated that the finite mixture models based on Burr and Inverse Burr component distributions perform well in the modeling of heavy-tail insurance data. Mixture models are able to capture the multimodality which is quite a common characteristic of insurance losses. Through an extensive simulation study, we assess the performance of three different methods in building the confidence intervals for high quantiles of the mixtures of Burr and Inverse Burr distributions. First, we provide mathematical justification for linking the tail of the k-Burr and k-Inverse Burr mixtures to the maximum domain of attraction of the Fréchet distribution which allows us to employ the Generalized Pareto Distribution (GPD) in the estimation of high quantiles and their corresponding confidence intervals. Then, we compare these results to those obtained using order statistics and the bootstrap methods. We also modified the existing Peak Over Threshold (POT) algorithm for the efficient computation of the confidence intervals in the upper tail of these mixture models. A real data set on Danish Fire Losses is used to illustrate the application of these methods in practice.

摘要

最近在单变量混合建模领域的研究表明，基于毛刺和逆毛刺分量分布的有限混合模型在重尾保险数据的建模中表现良好。混合模型能够捕捉多模态，这是保险损失的常见特征。通过广泛的模拟研究，我们评估了三种不同方法在构建毛刺和逆毛刺分布混合的高分位数的置信区间方面的性能。首先，我们为连接k -Burr 的尾部和k- 逆毛刺混合到 Fréchet 分布的最大吸引力域，这使我们能够使用广义帕累托分布 (GPD) 来估计高分位数及其相应的置信区间。然后，我们将这些结果与使用订单统计和引导方法获得的结果进行比较。我们还修改了现有的阈值峰值 (POT) 算法，以有效计算这些混合模型上尾部的置信区间。丹麦火灾损失的真实数据集用于说明这些方法在实践中的应用。