Compare methods

	Lorenz Curve	Atkinson Index	Gini Coefficient	Index of Dissimilarity	Palma Ratio
Field	Sociology	Sociology	Sociology	Sociology	Sociology
Family	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Year of origin	1905	1970	1912	1955	2011 (Palma's finding); 2013–2014 (the ratio)
Originator	Max Otto Lorenz	Anthony Barnes Atkinson	Corrado Gini	Otis Dudley Duncan & Beverly Duncan	Gabriel Palma; named by Cobham & Sumner
Type	Graphical representation of distributional inequality	Welfare-based, parameterized inequality index	Scalar measure of statistical dispersion / inequality	Index of evenness of two groups across units	Tail-ratio inequality measure
Seminal source	Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70), 209–219.	Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.	Ceriani, L., & Verme, P. (2012). The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini. The Journal of Economic Inequality, 10(3), 421–443.	Duncan, O. D., & Duncan, B. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20(2), 210–217.	Cobham, A., & Sumner, A. (2014). Is inequality all about the tails? The Palma measure of income inequality. Significance, 11(1), 10–13.
Aliases	Lorenz concentration curve, Lorenz diagram, cumulative share curve	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Gini index, Gini ratio, Gini concentration ratio, G	dissimilarity index, Duncan index, D index, segregation index	Palma index, Palma measure, top10/bottom40 ratio
Related	5	5	5	5	5
Summary	The Lorenz curve is a graphical device that displays the full shape of inequality in a distribution by plotting the cumulative share of a quantity (such as income) held by the cumulative share of the population, ranked from poorest to richest. Introduced by Max Lorenz in 1905, it underlies the Gini coefficient and provides the basis for ranking distributions by inequality when one curve lies entirely above another.	The Atkinson index is a welfare-based measure of inequality that incorporates an explicit, analyst-chosen parameter for how much society dislikes inequality. Introduced by Anthony Atkinson in 1970, it asks what fraction of total income could be discarded, under an equal distribution, while leaving social welfare unchanged — making the ethical judgement behind any inequality comparison transparent rather than hidden.	The Gini coefficient is the most widely used single-number summary of inequality in a distribution such as income or wealth. Introduced by the Italian statistician Corrado Gini in 1912, it equals twice the area between the Lorenz curve and the line of perfect equality, ranging from 0 when everyone has the same amount to a maximum approaching 1 when one unit holds everything.	The index of dissimilarity, often called the Duncan segregation index, measures how unevenly two groups — such as two racial or occupational groups — are distributed across a set of units like neighborhoods, schools, or occupations. It ranges from 0, when both groups have identical distributions across units, to 1, when the units are completely segregated, and has the intuitive interpretation of the share of one group that would have to relocate to achieve an even distribution.	The Palma ratio measures income inequality as the ratio of the income share held by the richest 10 percent of the population to the share held by the poorest 40 percent. It rests on the empirical regularity, documented by Gabriel Palma, that the middle deciles (5 through 9) capture a remarkably stable half of national income across countries, so that inequality is essentially a contest between the top and the bottom — the 'tails' of the distribution.