Compare methods

	Theil Inequality Decomposition	Atkinson Index	Gini Coefficient	Shapley Decomposition of Inequality
Field	Economics	Sociology	Sociology	Economics
Family	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Year of origin	1967	1970	1912	2013
Originator	Henri Theil (1967); decomposition class by Anthony Shorrocks (1980)	Anthony Barnes Atkinson	Corrado Gini	Anthony Shorrocks (working paper 1999; published 2013)
Type	Decomposable inequality measure	Welfare-based, parameterized inequality index	Scalar measure of statistical dispersion / inequality	Axiomatic decomposition procedure
Seminal source	Theil, H. (1967). Economics and Information Theory. Amsterdam: North-Holland. ISBN: 9780444814630	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.	Shorrocks, A. F. (2013). Decomposition procedures for distributional analysis: a unified framework based on the Shapley value. Journal of Economic Inequality, 11(1), 99–126.
Aliases	Theil Index, Theil's T and L, Generalized Entropy Decomposition, Within-Between Inequality Decomposition	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Gini index, Gini ratio, Gini concentration ratio, G	Shapley Decomposition, Shorrocks Shapley Decomposition, Factor Decomposition of Inequality, Shapley Value Distributional Decomposition
Related	3	5	5	4
Summary	The Theil index, introduced by Henri Theil in 1967 by importing Shannon's information theory into economics, measures income inequality as the divergence between each unit's income share and its population share. Its defining advantage is exact additive decomposability: total inequality splits cleanly into a within-group component (inequality inside each subgroup) and a between-group component (inequality between subgroup means). Theil's T and its companion L (mean log deviation) are the two best-known members of the generalized-entropy class, which Anthony Shorrocks showed in 1980 to be the only inequality measures that are additively decomposable in this way.	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 Shapley decomposition, formalized for distributional analysis by Anthony Shorrocks (in a widely circulated 1999 working paper, published in 2013), is a general procedure for attributing an inequality or poverty statistic to its contributing factors — income sources, population subgroups, or determinants. It borrows the Shapley value from cooperative game theory: each factor's contribution is its average marginal effect on the indicator across all possible orders in which factors could be eliminated. The result is an exact, symmetric, residual-free decomposition that applies to any indicator, even those (like the Gini) that have no natural analytic decomposition of their own.