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Comparison of the Gini and Zenga indexes using some theoretical income distributions abstract

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  • Katarzyna Ostasiewicz
  • Edyta Mazurek

Abstract

The most common measure of inequality used in scientific research is the Gini index. In 2007, Zenga proposed a new index of inequality that has all the appropriate properties of an measure of equality. In this paper, we compared the Gini and Zenga indexes, calculating these quantities for the few distributions frequently used for approximating distributions of income, that is, the lognormal, gamma, inverse Gauss, Weibull and Burr distributions. Within this limited examination, we have observed three main differences. First, the Zenga index increases more rapidly for low values of the variation and decreases more slowly when the variation approaches intermediate values from above. Second, the Zenga index seems to be better predicted by the variation. Third, although the Zenga index is always higher than the Gini one, the ordering of some pairs of cases may be inverted.

Suggested Citation

  • Katarzyna Ostasiewicz & Edyta Mazurek, 2013. "Comparison of the Gini and Zenga indexes using some theoretical income distributions abstract," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 23(1), pages 37-62.
    • Handle: RePEc:wut:journl:v:1:y:2013:p:37-62:id:1029
    DOI: 10.5277/ord130104
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    References listed on IDEAS

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    1. Ed Hopkins, 2008. "Inequality, happiness and relative concerns: What actually is their relationship?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(4), pages 351-372, December.
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    1. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    2. Chiara Gigliarano & Ugofilippo Basellini & Marco Bonetti, 2014. "Concentration in survival times and longevity: The log-scale-location family of failure time models," Working Papers 066, "Carlo F. Dondena" Centre for Research on Social Dynamics (DONDENA), Università Commerciale Luigi Bocconi.
    3. Chiara Gigliarano & Ugofilippo Basellini & Marco Bonetti, 2017. "Longevity and concentration in survival times: the log-scale-location family of failure time models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 254-274, April.

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