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Keywords:
Gini index; income distribution; share density function
Gini index; income distribution; share density function
Summary:
The expected value of the share density of the income distribution can be expressed in terms of the Gini index. The variance of the share density of the income distribution is interesting because it gives a relationship between the first and the second order Gini indices. We find an expression for this variance and, as a result, we obtain some nontrivial bounds on these Gini indices. We propose new statistics on the income distribution based on the higher moments of the share density function. These new statistics are easily computable from the higher order Gini indices. Relating these moments to higher order Ginis suggests new estimates on these quantities.
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
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