| Title:
|
Gini indices and the moments of the share density function (English) |
| Author:
|
Zizler, Petr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
167-175 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Gini index |
| Keyword:
|
income distribution |
| Keyword:
|
share density function |
| MSC:
|
62P20 |
| MSC:
|
91B15 |
| idZBL:
|
Zbl 06362219 |
| idMR:
|
MR3183470 |
| DOI:
|
10.1007/s10492-014-0047-5 |
| . |
| Date available:
|
2014-03-20T08:19:15Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143627 |
| . |
| Reference:
|
[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. 10.1257/jel.49.1.3 |
| Reference:
|
[2] Farris, F. A.: The Gini index and measures of inequality.Am. Math. Mon. 117 (2010), 851-864. Zbl 1203.91224, MR 2759359, 10.4169/000298910X523344 |
| Reference:
|
[3] Kleiber, C., Kotz, S.: A characterization of income distributions in terms of generalized Gini coefficients.Soc. Choice Welfare 19 (2002), 789-794. Zbl 1072.91621, MR 1935005, 10.1007/s003550200154 |
| . |
