Atkinson index: Difference between revisions

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In other words, the Atkinson index is the complement to 1 of the ratio of the [[Generalized mean|Hölder generalized mean]] of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the [[geometric mean]]).

Atkinson index relies onsatisfies the following axiomsproperties:

# The index is symmetric in its arguments: <math>A_\varepsilon(y_1,\ldots,y_N)=A_\varepsilon(y_{\sigma(1)},\ldots,y_{\sigma(N)})</math> for any permutation <math>\sigma</math>.

# The index is non-negative, and is equal to zero only if all incomes are the same: <math>A_\varepsilon(y_1,\ldots,y_N) = 0</math> iff <math>y_i = \mu</math> for all <math>i</math>.