Evaluation of an Alternative Functional Form to Fit the Lorenz Curve for the Concentration Index Calculation

Abstract

Precipitation concentration indices have become a popular tool for analyzing the structure of daily precipitation amounts. Among the existing indices, the concentration index (CI) is widely used. In calculating the CI, an important aspect is adjusting the Lorenz curve based on the observed precipitation data. Usually, the fit has been carried out with equations of the type y = axebx. However, in some research work, it has been observed that sometimes, the fit obtained only partially describes the behavior of the data. Thus, this work evaluated an alternative functional form to fit the Lorenz curve. For this, daily precipitation data from 44 climatological stations in Mexico were used to assess two equations for adjusting the Lorenz curve. Once the fit was made, the goodness of fit was evaluated to determine which of the functional forms best described the behavior of the data. Results showed that the two functional forms produced similar results for low precipitation concentrations. However, when the concentration increased, the alternative functional form generated results following the behavior of the observations. Thus, it is recommended to use the alternative functional form to avoid overestimations of the concentration of daily precipitation in areas where it is known that a high concentration occurs.