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</math>
where <math>y_{i}</math> is individual income (''i'' = 1, 2, ..., ''N'') and <math>\mu</math> is the [[mean]] income. With <math>\varepsilon=1</math>, we have <math>A=1-\exp(M)</math> where M is the [[mean log deviation]].
Atkinson index relies on the following axioms:
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# The index satisfies population replication axiom: if a new population is formed by replicating the existing population an arbitrary number of times, the inequality remains the same: <math>A_\varepsilon(\{y_1,\ldots,y_N\},\ldots,\{y_1,\ldots,y_N\})=A_\varepsilon(y_1,\ldots,y_N)</math>
# The index satisfies mean independence, or income homogeneity, axiom: if all incomes are multiplied by a positive constant, the inequality remains the same: <math>A_\varepsilon(y_1,\ldots,y_N) = A_\varepsilon( ky_1,\ldots,ky_N)</math> for any <math>k>0</math>.
# The index is subgroup decomposable.<ref>Shorrocks, AF (1980). The class of additively decomposable inequality indices. ''Econometrica'', 48 (3),
:: <math>
A_\varepsilon(y_{gi}: g=1,\ldots,G, i=1,\ldots,N_g) = \sum_{g=1}^G w_g A_\varepsilon( y_{g1}, \ldots, y_{g,N_g}) + A_\varepsilon(\mu_1, \ldots, \mu_G)
</math>
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* Sen A, Foster JE (1997) ''On Economic Inequality'', Oxford University Press, ISBN 978-0-19-828193-1. ([http://www.poorcity.richcity.org/oei/#Atkinson Python script] for a selection of formulas in the book)
* [http://www.wider.unu.edu/research/Database/en_GB/database/ World Income Inequality Database], from [[World Institute for Development Economics Research]]
* [http://www.census.gov/hhes/www/income/incineq/p60204/p60204txt.html Income Inequality,
== External links ==
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