Inequality measures for histograms

Abstract

While inequality or concentration measures are defined with reference to the distribution of a non-negative character among n individuals, most practical applications are effected on frequency distributions over k classes, namely on histograms, when thinking of the corresponding graphical representation. Concerning this type of applications, this paper examines: (1) the goodness of approximation – to indices computed on individual data – of the same indices worked out on histograms; (2) the meaning and properties of inequality indices that are functions of the only frequencies and quantities pertaining to the k classes. These two kinds of investigations have been addressed to classical concentration measures proposed by Gini and Pietra-Ricci.