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

Dan Ianculescu () and Cristian Gabriel Anghel ()
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Dan Ianculescu: Faculty of Hydrotechnics, Technical University of Civil Engineering Bucharest, Lacul Tei, nr.122–124, 020396 Bucharest, Romania
Cristian Gabriel Anghel: ACL Hydro Engineering Solutions SRL, 022846 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 21, 1-11

Abstract: 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.

Keywords: flood; extreme events; Weibull; L-moments; K-moments; heavy-tail behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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