Decomposition and normalization of absolute differences, when positive and negative values are considered: applications to the Gini coefficient

We show how the absolute differences approach is particularly effective to interpret the Gini coefficient (G) when a distribution includes both positive and negative values. Either in erasing units having negative values, or in transforming negative values into zero, a significant variability fraction can be lost. When including negative values, instead of correcting G, to maintain it lower than 1, the standard G should be kept to compare the variability among different situations; a recent normalization, Gp, can be associated to G, to evaluate the variability percentage inside each situation.