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Patallurgist (talk | contribs) fix inaccurate formula -- Atkinson is not additively decomposable |
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# The index is (non-additively) subgroup decomposable and the corresponding generalized entropy index is ''additively'' subgroup decomposable.<ref>Shorrocks, AF (1980). The class of additively decomposable inequality indices. ''Econometrica'', 48 (3), 613–625, {{doi|10.2307/1913126}}</ref> This means that overall inequality in the population can be computed as the sum of the corresponding GE indices within each group, and the GE index of the group mean incomes:
::: <math>
GE(\alpha; y_{gi}: g=1,\ldots,G, i=1,\ldots,N_g) = \sum_{g=1}^G w_g GE(\alpha; y_{g1}, \ldots, y_{gN_g}) + GE(\
</math>
::where <math>g</math> indexes groups, <math>i</math>, individuals within groups, <math>\mu_g</math> is the mean income in group <math>g</math>, and the weights <math>w_g</math> depend on <math>\mu_g, \mu, N</math> and <math>N_g</math>. The class of the additively-decomposable inequality indices is very restrictive; in fact, only the generalized entropy indices are additively decomposable. Many popular indices, including [[Gini index]], do not satisfy this property.
== See also ==
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