Comparison of the Gini and Zenga indexes using some theoretical income distributions abstract

The most common measure of inequality used in scientific research is the Gini index. In 2007 Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper we want to compare the Gini and Zenga indexes, calculating these quantities for a few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination of these indexes, we have observed three main differences. First, the Zenga index increases more rapidly for low values of the variation and decreases more slowly when the variation approaches intermediate values from above. Second, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always greater than the Gini index, the ordering of some pairs of cases may be inverted.