Innovative Explicit Relations for Weibull Distribution Parameters Based on K-Moments

Accurate estimation of probability distribution parameters is fundamental in frequency analyses of extreme hydrological and meteorological events. The reliability of such analyses largely depends on the estimation method adopted and on the availability of explicit relationships for parameter calculation. However, many parameter estimation methods are not yet implemented in specialized software, which limits their practical applicability. This study presents innovative explicit relationships for estimating the parameters of the Weibull distribution—one of the most widely used models in hydrology and environmental sciences—using the Known Moments method (K-moments). The proposed approximations, based on rational functions, enable the estimation of Weibull parameters (particularly the shape parameter) with admissible relative errors below 1%. The performance of the K-moments method was demonstrated through representative case studies from Romanian hydrology. The results show that the developed relationships significantly simplify the practical implementation of the Weibull distribution in frequency analysis using K-moments, ensuring both high accuracy and computational efficiency.