Introduction

Abstract

Gini’s mean difference (hereafter, GMD) was first introduced by Corrado Gini in 1912 as an alternative measure of variability. GMD and the parameters which are derived from it (such as the Gini coefficient, also referred to as the concentration ratio) have been in use in the area of income distribution for almost a century, and there is evidence that the GMD was introduced even earlier (Harter, 1978). In other areas it seems to make sporadic appearances and to be “rediscovered” again and again under different names. It turns out that GMD has at least 14 different alternative representations. Each representation can be given its own interpretation and naturally leads to a different analytical tool such as L₁ metric, order statistics theory, extreme value theory, concentration curves, and more. Some of the representations hold only for nonnegative variables while others need adjustments for handling discrete distributions. On top of that, the GMD was developed in different areas and in different languages. Corrado Gini himself mentioned this difficulty (Gini, 1921). Therefore in many cases even an experienced expert in the area may fail to identify a Gini when he or she sees one.