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Gini index; income distribution; share density function

References:

[1] Atkinson, A. B., Piketty, T., Saez, E.: **Top incomes in the long run of history**. Journal of Economic Literature 49 (2011), 3-71, http://www.nber.org/papers/w15408 DOI 10.1257/jel.49.1.3

[2] Farris, F. A.: **The Gini index and measures of inequality**. Am. Math. Mon. 117 (2010), 851-864. DOI 10.4169/000298910X523344 | MR 2759359 | Zbl 1203.91224

[3] Kleiber, C., Kotz, S.: **A characterization of income distributions in terms of generalized Gini coefficients**. Soc. Choice Welfare 19 (2002), 789-794. DOI 10.1007/s003550200154 | MR 1935005 | Zbl 1072.91621