Robust fitting of the generalized Pareto distribution for extreme precipitation modeling: a case study in Japan

Abstract This study introduces a robust-efficient method for estimating the parameters of the generalized Pareto distribution (GPD), based on the probability integral transform. The probability integral transform estimator (PITE) is designed to enhance robustness in the presence of outliers, a frequent challenge in modeling extreme events. We also study the properties of PITE, including its efficiency and its robustness based on score function and breakdown point, demonstrating its ability to handle extreme data with minimal sensitivity to outliers. In addition, PITE offers computational simplicity, making it accessible for practical applications. Monte Carlo simulations indicate that the PITE family provides a flexible balance between robustness and efficiency: high-efficiency versions perform comparably to traditional estimators for uncontaminated data, while more robust versions often yield smaller deficiencies in simulated scenarios with data contamination. Applied alongside the peaks over threshold approach, PITE effectively models the tail behavior of extreme precipitation events. The method is applied to daily precipitation data from 12 meteorological stations in southern Japan, a region highly susceptible to extreme rainfall due to typhoons and complex climatic factors. Using PITE, GPD parameters are estimated, and return levels for 5-, 10-, 25-, 50-, 100-, and 200-year periods are calculated. The results reveal significant regional variability in extreme precipitation, with stations such as Naze, Miyazaki, and Kumamoto displaying particularly high return levels, indicative of their vulnerability to intense rainfall. The robust application of PITE provides critical insights for flood risk management in southern Japan, particularly in typhoon-prone settings where storm-driven extremes can act as potential outliers, highlighting the importance of localized strategies to mitigate the impact of extreme precipitation events.