Secondo fascicolo del 2015
Asymptotic properties of some estimators for Gini and Zenga
inequality measures: a simulation study
by Alina Jedrzejczak
It is well known that unequal income distribution, yielding poverty, stratification and polarization, can be a serious economic and social problem. The reliable inequality analysis of both, total population of households and subpopulations classified by different characteristics, can be a helpful piece of information for economists and social policy- makers. Therefore, it seems especially important to present reliable estimates of income inequality measures for a population of households in different divisions. Among many income inequality measures the Gini index based on the Lorenz curve is the most popular one. Another interesting measure of income inequality is the Zenga index proposed in 1984, based on the relation between income and population quantiles. In the paper some nonparametric estimators of Gini and Zenga inequality measures are presented and analyzed from a point of view of their statistical properties. In particular, the bias, dispersion and normality of the estimators are considered. The Monte Carlo experiments include the cases of heavy-tailed and light-tailed distributions as theoretical models. Finally, the estimators are applied to the data on income distributions in Poland.
Joint decomposition by subpopulations and sources of the Zenga
inequality index I(Y)
by Michele Zenga
Keywords: Zenga Inequality Index, Income Inequality, Joint Decomposition by Subpopulations and Sources, Point and Synthetic Inequality Indexes.
Bipolar distributions in fuzzy sets theory
by Donata Marasini, Piero Quatto, Enrico Ripamonti
In this paper we consider the problem of measuring latent variables with ordinal scales and we put forward an original approach to this issue, which combines the use of Intuitionistic Fuzzy Sets with the calculation of bipolar means and bipolar distributions. Intuitionistic Fuzzy theory allows a researcher to model the degree of membership and non-membership to a certain fuzzy set, as well as the residual uncertainty. It is fundamental, for decision making, to properly model such source of variability. We focus on the definition of uncertainty, using bipolar distributions and introducing Intuitionistic Bipolar Fuzzy Sets. This allows us to distinguish between a negative and a positive component of uncertainty, which represents a novelty in Intuitionistic Fuzzy analysis. We apply this method to a national evaluation survey (The Magellano Project) proposed by the Italian Ministry of Public Administration, aimed at involving employees in management decision.
Tests and confidence intervals for geometric mean from one and
two populations: a unified approach
by Elsayed A.H. Elamir
The geometric mean is a type of mean which indicates the central tendency of a set of numbers by using the product of their values and has many applications in several fields such as proportional growth, signal processing and spectral flatness. A unified approach to tests and confidence intervals for geometric mean in one population and two populations are introduced based on lognormal distribution under no conditions on the parent population. The distribution of the ratio of two geometric means is derived without any assumption on the distribution of the data. Three applications in banking, business and medicine are used to illustrate the benefits of the method.