Gini indices and the moments of the share density function

Petr Zizler

Applications of Mathematics (2014)

  • Volume: 59, Issue: 2, page 167-175
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Zizler, Petr. "Gini indices and the moments of the share density function." Applications of Mathematics 59.2 (2014): 167-175. <http://eudml.org/doc/261097>.

@article{Zizler2014,
abstract = {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.},
author = {Zizler, Petr},
journal = {Applications of Mathematics},
keywords = {Gini index; income distribution; share density function; Gini index; income distribution; share density function},
language = {eng},
number = {2},
pages = {167-175},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Gini indices and the moments of the share density function},
url = {http://eudml.org/doc/261097},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Zizler, Petr
TI - Gini indices and the moments of the share density function
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 167
EP - 175
AB - 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.
LA - eng
KW - Gini index; income distribution; share density function; Gini index; income distribution; share density function
UR - http://eudml.org/doc/261097
ER -

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