A Class of Bonferroni Inequality Indices

Abstract

The purpose of this paper is to propose a family of inequality measures obtained from the Bonferroni curve as a distribution function. This family characterizes the income distribution, given the mean income, as well as other families considered in this paper. Although all of the families show a clear formal analogy and are mutually determined, their elements include very different value judgments for measuring inequality and social welfare. Normative aspects are analyzed by means of the preference distributions associated to the indexes. This allows us to compare the indexes, and in some cases, rank them according to their degree of inequality aversion, as well as studying their behavior regarding different principles of transfer.

Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure

“…The Bonferroni curve (Bonferroni 1930) is a minor modification of the Lorenz curve based on the comparison between partial means and the general mean of a certain distribution. It is constructed by considering as abscissa the cumulative proportion of individuals arranged in increasing size of their incomes and as ordinate the corresponding mean density of their income (see Giorgi andCrescenzi 2001 andImedio-Olmedo et al 2011 for more information). Alternatively, the Zenga curve is as well a graphic representation of inequality.…”

On a Distance Function-Based Inequality Measure in the Spirit of the Bonferroni and Gini Indices

“…This paper has been a variation on the theme of the Bonferroni inequality index, which has been subjected to rigorous analysis by, among others, Barcena and Imedio (2000), Giorgi and Crescenzi (2001), Chakravarty (2007), and Imedio-Olmedo et al (2011).…”

“…At least four important contributions to reviving interest in, to interpreting, to characterizing, and to analyzing the properties of, the Bonferroni inequality measure are the papers by Barcena and Imedio (2000), Giorgi and Crescenzi (2001), Chakravarty (2007), and Imedio-Olmedo, Barcena-Martin and Parrado-Gallardo (2011). Also of relevance is a brief note by the present author (Subramanian 1989) which advanced what was called a 'simple transfer-sensitive index of inequality', in complete ignorance of the fact that the index in question was Bonferroni's!…”

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

“…Giorgi and Crescenzi (2001), and Chakravarty and Muliere (2004) propose poverty measures based on the fact that the Bonferroni index exhibits greater sensitivity on lower levels of the income distribution than the Gini index. A general class of inequality measures inspired by the Bonferroni index has been explored by Imedio-Olmedo et al (2011). Giorgi (1998) provides a list of Bonferroni's publications.…”