Giovanni Maria Giorgi

Income Inequality Measurement: The Statistical Approach

The problem of measuring income inequality can be traced back to the end of the last century. (1895), for example, discussed the topic in a study on personal income distribution which, it seems, began as a consequence of a diatribe between the author himself and Italian and French socialists on the way and on the instruments with which a more equal distribution could be reached. Pareto based his work mainly on fiscal data and interpreted the parameter α of the model he proposed as an income inequality measure.

Bonferroni and Gini indices for various parametric families of distributions

SummaryThe Bonferroni index (BI) and Bonferroni curve (BC) have assumed relief not only in economics to study income and poverty, but also in other fields like reliability, demography, insurance and medicine. Besides, the increasingly frequent comparison with the Lorenz curve (LC) and Gini index (GI) both in theoretical and applied studies has driven us to derive explicit expressions for BI, BC, GI and LC for some thirty five continuous distributions. It is expected that these expressions could provide a useful reference and encourage further research within the aforementioned fields.

Corrado Gini: the man and the scientist

SummaryThe paper discusses the times in which Corrado Gini lived in an attempt to enrich our picture of him by adding some further information to his complex personality.

A fuzzy logic approach to poverty analysis based on the Gini and Bonferroni inequality indices

In the poverty analysis framework, a great deal of attention has been paid to the poverty measurement in terms of monetary variables, such as income or consumption. In this context, a relevant open problem is connected with the distinction between poor and non-poor. In fact, the concept of poverty is rather vague and cannot be defined in a clear way. In this respect, following a fuzzy logic approach, some new poverty measures are proposed. In particular, the fuzzy extension of two existing poverty measures based on the Gini and Bonferroni inequality indices is provided. Some synthetic and real applications are given in order to show how the proposed poverty measures work.

Bayesian estimation of the Bonferroni index from a Pareto-type I population

SummaryThe Bonferroni index (B) is a measure of income and wealth inequality, and it is particularly suitable for poverty studies. Since most income surveys are of a sample nature, we propose Bayes estimators ofB from a Pareto/I population. The Bayesian estimators are obtained assuming a squared error loss function and, as prior distributions, the truncated Erlang density and the translated exponential one. Two different procedures are developed for a censored sample and for income data grouped in classes.

THE GINI CONCENTRATION INDEX: A REVIEW OF THE INFERENCE LITERATURE

More than a century ago, Corrado Gini proposed his well-known concentration index for measuring the degree of inequality in the distribution of income and wealth. His index is still extremely relevant and widely used in several fields of research and application. In this paper, we focus on the inferential properties of the Gini index, and discuss the main directions of analysis proposed in the literature. The aim of the paper is to provide a comprehensive review of the main developments on the inferential aspects of the Gini concentration ratio. We feel that this work can provide a valuable contribution to those scholars who are approaching the large amount of literature on the inferential properties of the Gini index.