Atkinson index

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Anthony Barnes Atkinson developed various indexes. In statistics the Atkinson indexes are a measures of income inequality. The indexes can be turned into normative measures once we impose a coefficient $\varepsilon$ to weight incomes.

The formulas are:

$A=1-\frac{1}{\mu}\left(\frac{1}{N}\sum_{i=1}^{N}y_{i}^{1-\varepsilon}\right)^{1/(1-\varepsilon)} \forall \varepsilon>0,\varepsilon \neq 1$

and:

$A=1-\frac{1}{\mu}\left(\prod_{i=1}^{N}y_{i}\right)^{1/N}\ \mbox{for}\ \varepsilon=1,$

where $y i$ is individual income (i = 1, 2, ..., N) and $μ$ is the mean income.

An entropy measure from Atkinson can be computed from the Theil index (example without using $\varepsilon$ )

$\mbox{Atkinson index} = 1 - e^{-\mbox{Theil index}}.\,$

[edit] See also

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Category: Econometrics

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