An automated threshold selection procedure for generalized Pareto distribution with application to rainfall dataset

In hydrological datasets, particularly rainfall, the study of extreme values is crucial. The appropriate analysis of such datasets can provide vital information about the return levels of extreme rainfall, which can play a significant role in disaster prevention. In many situations, the GPD has been a well-respected option for studying extreme data; nonetheless, there are still concerns about the GPD's threshold selection method. The commonly used Mean Residual Life (MRL) plot technique for threshold selection in Generalized Pareto Distribution (GPD) analysis suffers from subjectivity and requires extensive prior knowledge, limiting its reproducibility. This paper introduces a straightforward, computationally inexpensive, and automated procedure for threshold selection. By employing interval-based candidate thresholds and goodness-of-fit (GOF) tests, the proposed method determines the optimal threshold that maximizes the p-value, enhancing objectivity and accuracy. Several combinations of estimation methods and GOF tests were investigated, with the CVM-Lmoment combination emerging as the most robust. Through extensive simulation studies, our approach demonstrated significant improvements in reducing bias and RMSE compared to traditional methods. The application of the proposed methodology to a rainfall dataset from South-West England confirmed its robustness and practical utility, making it a valuable tool for extreme value modeling and disaster management.