Scomposizione per sottopopolazioni dell'indice di Bonferroni

In this thesis it is suggested a decomposition by subpopulation of the Bonferoni index. This purpose is attained at first suggesting a definition of the Bonferroni index for data expressed in terms of frequency distribution and then, using the approach proposed by Zenga (Zenga, 2012) for the decomposition of his index, it follow a decomposition by subpopulation of the Bonferroni index in two steps. The Bonferroni and Zenga indexes, as well as the Gini index (Gini, 1914), are implemented in two steps: in the first step, point measures are made, whereas in the second steps, a synthetic index is obtained averaging the point measures. Until now the proposals suggested for the decompositions of the Gini and Bonferroni indexes were based on the decomposition of the synthetic indexes; in this works, the decomposition by subpopulation is based instead on the decompositions of the point measures. Following this approach, in the first part of the suggested procedure, an additive decomposition is obtained and the contributions of each subpopulation to the point inequality measure, evaluated on the whole population, is computed. From this decomposition, other two decomposition terms are deduced: a within term, that is a measure of inequality evaluated within a subpopulation, and a between term that informs on the inequality derived from the comparison between different subpopulation. In the second part of this work, exploiting these decomposition, an additive decomposition is obtained for the synthetic index. Finally, the methodology proposed is applied on data on the net disposable households income provided by Banca d’Italia in 2014 and comparison among inequality indexes are made.