New Parametric Approach for Modeling Hydrological Data: An Alternative to the Beta, Kumaraswamy, and Simplex Models

Abstract

We propose a new approach of continuous distributions in the unit interval, focusing on hydrological applications. This study presents the innovative two-parameter model called modified exponentiated generalized (MEG) distribution. The efficiency of the MEG distribution is evidenced through its application to 29 real datasets representing the percentage of useful water volume in hydroelectric power plant reservoirs in Brazil. The model outperforms the beta, simplex, and Kumaraswamy (KW) distributions, which are widely used for this type of analysis. The connection of our proposal with classical distributions, such as the Fréchet and KW distribution, broadens its applicability. While the Fréchet distribution is recognized for its usefulness in modeling extreme values, the proximity to KW allows a comprehensive analysis of hydrological data. The simple and tractable analytical expressions of the MEG's density and cumulative and quantile functions make it computationally feasible and particularly attractive for practical applications. Furthermore, this work highlights the relevance of the related reflected model: the reflected modified exponentiated generalized distribution. This contribution is expected to improve the statistical modeling of hydrological phenomena and provide new perspectives for future scientific investigations.