An In-Depth Statistical Analysis of the Pearson Type III Distribution Behavior in Modeling Extreme and Rare Events
Cristian Gabriel Anghel, Dan Ianculescu
Abstract
Statistical distributions play a crucial role in water resources management and civil engineering, particularly for analyzing data variability and predicting rare events with extremely long return periods (e.g., T = 1000 years, T = 10,000 years). Among these, the Pearson III (PE3) distribution is widely used in hydrology and flood frequency analysis (FFA). This study aims to provide a comprehensive guide to the practical application of the PE3 distribution in FFA. It explores five parameter estimation methods, presenting both exact and newly developed approximate relationships for calculating distribution parameters and frequency factors. The analysis relies on data from four rivers with varying morphometric characteristics and record lengths. The results highlight that the Pearson III distribution, when used with the L-moments method, offers the most reliable quantile estimates, characterized by the smallest biases compared to other methods (e.g., 31% for the Nicolina River and, respectively, 5% for the Siret and Ialomita Rivers) and the highest confidence in predicting rare events. Based on these findings, the L-moments approach is recommended for flood frequency analysis to improve the accuracy of extreme flow forecasts.