Using Negative Power Transformation to Model Block Minima

This study proposes a novel transformation method for analyzing block minima using the generalized extreme value distribution (GEVD). The negative power transformation (NPT), which includes a tunable hyperparameter and reduces to the reciprocal transformation (RT) when set to 1, improves the accuracy and robustness in estimating long-term return levels (RL). Compared to traditional methods, the NPT-GEVD demonstrates lower bias, standard errors, and root mean square errors in Monte Carlo simulations. Furthermore, the NPT-GEVD provides consistent RL estimates with improved robustness across varying parameterizations and sample sizes, mainly when using L-moments for small datasets. The application of the NPT-GEVD to rainfall data from South Korea revealed that the RLs for detecting hourly cumulative rainfall threshold levels varied from 30 min to over 4 h, depending on the location and threshold. This research underscores the value of advanced transformation techniques in environmental risk management, offering critical insights for flood prediction and mitigation strategies in climate change.