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

Ostasiewicz K., Mazurek E.

Operations Research and Decisions

2013

Vol. 23, No. 1

37--62

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.

Agricultural sustainability in a simple social-ecological system

Ostasiewicz K., Magnuszewski P.

Operations Research and Decisions

2010

Vol. 20, No. 3-4

81-94

There is a growing consciousness of the complexity and universality of interactions between social and ecological systems. Here we investigate a simple social-ecological model of land cultivation. It is shown that even very simple rules of land-use and an ecosystem’s dynamics can generate a variety of possible stationary states. In particular, the possibility of the existence of "desirable" stationary states is examined. These desirable states are understood in the sense of sustainable development, that is, profitable for farmers and non-degrading for ecosystems. It turns out that the existence of such states can depend strongly on the parameters that are under a government's control, e.g. subsides, and others. Although real systems can reveal much more complex and counterintuitive behaviour, such a "toy model" can at least give some insight, help to realize the range of possible scenarios and improve our intuition about what might happen in real systems.