Modeling excess remains to be an important topic in insurance data modeling. Among the alternatives of modeling excess, the Peaks Over Threshold (POT) framework with Generalized Pareto distribution (GPD) is regarded as an efficient approach due to its flexibility. However, the selection of an appropriate threshold for such framework is a major difficulty. To address such difficulty, we applied several accumulation tests along with Anderson-Darling test to determine an optimal threshold. Based on the selected thresholds, the fitted GPD with the estimated quantiles can be found. We applied the procedure to the well-known Norwegian Fire Insurance data and constructed the confidence intervals for the Value-at-Risks (VaR). The accumulation test approach provides satisfactory performance in modeling the high quantiles of Norwegian Fire Insurance data compared to the previous graphical methods.

翻译：超额建模仍是保险数据建模中的重要课题。在超额建模的多种替代方法中，基于广义帕累托分布（GPD）的超阈值（POT）框架因其灵活性而被视为一种高效方法。然而，为该框架选择合适的阈值是主要难点。为解决此难题，我们应用了多种积累检验及安德森-达林检验来确定最优阈值。基于所选阈值，可拟合出具有估计分位数的GPD模型。我们将该流程应用于著名的挪威火灾保险数据，并构建了风险价值（VaR）的置信区间。与先前的图形方法相比，积累检验方法在建模挪威火灾保险数据的高分位数方面表现令人满意。