  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.
