Beautiful Gini

Abstract

You may very well be familiar with the Gini Coefficient, also known as the Gini index: a quantitative gauge with which socioeconomic inequality is measured, e.g. income disparity and wealth disparity. However, you may not know that the Gini Coefficient is an exquisite mathematical object. Enter this review paper—whose aim is to showcase (some of) the mathematical beauty and riches of the Gini Coefficient. The paper does so, in a completely self-contained manner, by illuminating the Gini Coefficient from various perspectives: Euclidean geometry vs. grid geometry; maxima and minima of random variables; statistical distribution functions; the residual lifetime and the total lifetime of renewal processes; increasing and decreasing failure rates; socioeconomic divergence from perfect equality; and weighted differences of statistical distribution functions. Together, these different perspectives offer a deep and comprehensive understanding of the Gini Coefficient. In turn, a profound understanding of the Gini Coefficient may lead to novel ‘Gini applications’ in science and engineering—such as recently established in the multidisciplinary field of restart research.