Comparative study of threshold selection methods in the generalised Pareto distribution with application to rainfall datasets

Extreme rainfall events pose significant challenges for flood risk management and infrastructure planning, necessitating robust statistical tools for accurate risk assessment. This study rigorously compares four threshold selection methods for the generalised Pareto Distribution across five distinct rainfall datasets from Southwest England, New Zealand, Bangladesh, Singapore, and the US (Seattle). The methods evaluated include the classical mean residual life plot, a goodness-of-fit p-value-based approach, a parameter stability method, and an automated procedure that combines goodness-of-fit testing with the method of estimation. Return level estimates for 10-, 50-, and 100-year events were estimated, with uncertainties quantified via a bootstrap percentile method. The results reveal that, while each method has its merits, the approach based on goodness-of-fit criteria coupled with the method of estimation generally provides a slight edge. It consistently delivers logically interpretable thresholds that balance bias and variance effectively, particularly in managing datasets with a high prevalence of zero rainfall events. Although alternative methods occasionally yield narrower confidence intervals, they sometimes sacrifice the accurate representation of tail behaviour. Importantly, the study does not dismiss the reliability of other techniques; rather, it underscores that threshold selection is inherently dataset dependent. Overall, this study proposes that while each method offers specific advantages depending on the dataset's characteristics, the approach that integrates goodness-of-fit testing with estimation techniques consistently achieves a favourable balance between simplicity, interpretability, and statistical robustness for threshold selection in generalised Pareto modelling of rainfall extremes. These findings highlight the importance of methodological adaptability and contribute valuable insights toward improving flood risk assessments under diverse climatic conditions.