Editing Gini coefficient (section)

== Generalized inequality indices ==
{{See also|Generalized entropy index}}

The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, <math>r_j = x_j / \overline{x}</math>, equals 1 for all j units in some population (for example, there is perfect income equality when everyone's income <math>x_j</math> equals the mean income <math>\overline{x}</math>, so that <math>r_j=1</math> for everyone). Measures of inequality, then, are measures of the average deviations of the <math>r_j=1</math> from 1; the greater the average deviation, the greater the inequality. Based on these observations the inequality indices have this common form:<ref>{{Cite journal |last=Firebaugh |first=Glenn |year=1999 |title=Empirics of World Income Inequality |journal=American Journal of Sociology |volume=104 |issue=6 |pages=1597–1630 |doi=10.1086/210218 |s2cid=154973184 }}. See also {{Cite book |chapter=Inequality: What it is and how it is measured |first=Glenn |last=Firebaugh |author-mask=3 |title=The New Geography of Global Income Inequality |location=Cambridge, MA |publisher=Harvard University Press |year=2003 |isbn=978-0-674-01067-3}}</ref>

:<math>\text{Inequality} = \sum_j p_j \, f(r_j), </math>

where ''p''<sub>''j''</sub> weights the units by their population share, and ''f''(''r''<sub>''j''</sub>) is a function of the deviation of each unit's ''r''<sub>''j''</sub> from 1, the point of equality. The insight of this generalized inequality index is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the ''r''<sub>''j''</sub>) from 1.