Including the asymmetry of the Lorenz curve into measures of economic inequality

The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by attaching weights to the distances between the Lorenz curve and the 45-degree line. The measure is equivalent to the Gini if the distribution is symmetric. The alternative measure of inequality inherits good properties from the Gini but is more sensitive to changes in the extremes of the income distribution.