A New Proposal for Optimizing Maximum Hydrological Events Fitting with Flexible TCEV Distribution

Abstract. Accurate characterization of extreme hydrological events is critical for flood risk assessment and hydraulic engineering design, particularly in the high-value cumulative distribution function (CDF, F(x)) range that governs design extremes. Hydrological records often consist of mixed populations of ordinary and extreme events, leading to a pronounced “dog-leg effect” that limits the applicability of conventional extreme-value distributions such as the Gumbel and Log-Pearson Type III. Although the Two-Component Extreme Value (TCEV) distribution is conceptually well suited to such mixed populations, its practical application is constrained by subjective parameter initialization, uniform weighting schemes that underrepresent right-tail extremes, and evaluation metrics with limited tail sensitivity. In this study, we propose a new fitting method for the TCEV distribution, SR-MWS, which uses piecewise linear fitting for stable initial parameters, right-tail-oriented weighting for extreme events, and a partitioned scoring framework to evaluate global and tail performance. The results of the hydrological dataset indicate that SR-MWS consistently outperforms existing TCEV estimation methods in accuracy and robustness. Further experiments based on simulated data show that this method achieves better global fitting performance while maintaining tail accuracy comparable to the Peaks-Over-Threshold (POT) method, and is significantly better than generalized extreme value (GEV) and Gumbel distributions in capturing extremes. By reducing subjectivity and enhancing robustness, the proposed method provides an automated framework for extreme-event modeling applicable to other mixed-population extreme-value problems.