Where does the Gini Coefficient Spreadsheet Computation on Wikipedia come from?

on Wikipedia there is a page called income inequality metrics and there is a table that explains how to compute a few, for example the well-known Gini Coefficient. Please find this approach under this link: https://en.wikipedia.org/wiki/Income_inequality_metrics. I used the formula before because I tested it against other approaches and it yields the very same results.

However I cannot trace back its origins nor does it compare exactly to other approaches on the Gini Coefficient Wikipedia page: https://en.wikipedia.org/wiki/Gini_coefficient. At least not as far as I understand. It is maybe from a Amartya Sen Book "On Economic Inequality, expanded edition with a substantial annexe, ISBN 0-19-828193-5", that is linked previous to the spreadsheet computations but I cannot verify because it is not available for free. Does anybody recognize the approach and maybe can point me to some literature or can show me the mathematical equivalence to other approaches? I'll just quickly outline how they do it there.

They have $$\ A_i$$ that is each particular population segment.

They also have $$\ E_i$$ the income per each group.

Then they build the income per person $$\ E_i/A_i$$. Afterwards a relative deviation factor: $$\ D_i = E_i/ΣE - A_i/ΣA$$

A cumulated income factor $$\ K_i = E_i + K_{i-1}$$.

Then they build a "Gini- or G-Factor", that I cannot relate to any other approach the following way $$\ G_i = (2 * K_i - E_i) * A_i$$.

In the end the Gini Coefficient is defined as $$\ Gini Coefficient = 1 - ΣG/ΣA/ΣE$$.

Thank you I appreciate any help.

• Could you clarify which numbers from the Wikipedia article exactly you want to reproduce? – E. Sommer Dec 5 '18 at 14:18
• Hi I do not want to reproduce any number I want to understand the equations above, understand their equivalence to other GINI approaches and/or be referred to studies that officially explain this approach. – Yan91 Dec 5 '18 at 14:21
• OK this looks to me like the formula shown under 'other approaches' in your second link, where the Lorentz curve is approximated – E. Sommer Dec 5 '18 at 17:05