Statistical Study of Rainfall Control: The Dagum Distribution and Applicability to the Southwest of Spain

Abstract

It is of vital importance in statistical distributions to fit rainfall data to determine the maximum amount of rainfall expected for a specific hydraulic work. Otherwise, the hydraulic capacity study could be erroneous, with the tragic consequences that this would entail. This study aims to present the Dagum distribution as a new statistical tool to calculate rainfall in front of frequent statistical distributions such as Gumbel, Log-Pearson Type III, Gen Extreme Value (GEV) and SQRT-ET max. The study was performed by collecting annual rainfall data from 52 meteorological stations in the province of Badajoz (Spain), using the statistical goodness-of-fit tests of Anderson–Darling and Kolmogorov–Smirnov to establish the degree of fitness of the Dagum distribution, applied to the maximum annual rainfall series. The results show that this distribution obtained a flow 21.92% greater than that with the traditional distributions. Therefore, in the Southwest of Spain, the Dagum distribution fits better to the observed rainfall data than other common statistical distributions, with respect to precision and calculus of hydraulics works and river flood plains.