Talk:Generalized entropy index

Transformation seems wrong

"The transformation is $A=1-e^{-GE}$ " seems wrong. Defining

$\phi ={\frac {1}{N}}\sum _{i=1}^{N}\left({\frac {y_{i}}{\mu }}\right)^{\alpha }$

I get (using $\varepsilon =1-\alpha$):

$A=1-\phi ^{1/\alpha }$

and

$GE={\frac {\phi -1}{\alpha (\alpha -1)}}$

which won't give the above relationship. (A is the Atkinson index) PAR (talk) 02:25, 25 May 2014 (UTC)

It is definitely correct for a GE index of order 0.

See here: https://www.academia.edu/1816869/A_note_on_the_relationship_between_the_Atkinson_index_and_the_generalised_entropy_class_of_decomposable_inequality_indexes_under_the_assumption_of_log-normality_of_income_distribution_or_volatility

The case of general $\epsilon$ also seems wrong, and disagrees with the definition given here: https://en.wikipedia.org/wiki/Atkinson_index

I believe it should be $A=1-{\sqrt[{\alpha }]{GE\varepsilon (\varepsilon -1)+1}}$.

Where does the 1/(alpha * (alpha - 1)) come from?

In the denominator of the fraction that is a factor of the constant by which the sum is multiplied, where does the...

alpha * (alpha - 1) come from? What's the explanation for why that's there? — Preceding unsigned comment added by 97.82.116.234 (talk) 03:47, 30 April 2022 (UTC)

Focus on income inequality seems restrictive

This is a comment about the focus/tone of this article, rather than any element of the content per se. It seems that generalized entropies have far-ranging applications (information theory, income inequality, biological diversity measures) and this article implies that their primary application or the domain in which they make the most sense is in defining income inequality. Would be great if future edits made clear that income inequality is an *example* and a topic of study where theoretical and conceptual advances on this topic have been made, but that generalized entropies have a wider array of potential applications. Muniche (talk) 11:46, 14 July 2022 (UTC)