The Lorenz Curve and the Concentration Curve
The Lorenz and the concentration curves play important roles in the areas of GMD and the related measures such as Gini covariance, Gini correlation, Gini regression, and more. In this chapter we introduce the curves, discuss their properties, and show their connections to the Gini world. In addition, in order to be able to analyze the parallel concepts that are common in the variance world we investigate the equivalents of the Lorenz and the concentration curves that are relevant to the variance and the covariance, respectively. Those parallel curves share some properties among themselves. Therefore one can deduct from the concentration curve about some properties of the covariance and not only about the Gini covariance. In addition we present the relationships between the concepts of second-degree stochastic dominance and welfare dominance on one hand and the concentration and Lorenz curves on the other hand. These relationships enable the Gini methodology to serve as an analytical tool for statistical analyses and to be compatible with economic theory, a property that holds for the variance as well, but only for specific distributions.
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