On Corrado Gini’s 1932 paper “Intorno alle curve di concentrazione”. A selection of translated excerpts

Abstract

Metron, continuing its editorial policy of diffusion of the main scientific results reached by the so-called Italian Statistical School in the first half of the XXth century, publishes an English synthetic version of the article “Intorno alle curve di concentrazione” written by Corrado Gini in 1932, in the occasion of the 50th anniversary of his death. The main focus of the paper is the study of the concentration curve, with special emphasis on its fundamental features and properties and on the relationship with other relevant curves. In particular, the Author aimed at investigating on the goodness of the approximation of the concentration area, and therefore of the concentration ratio, both from a methodological and an empirical point of view, in some specific cases in which Cotes quadrature formula can be applied. One of the most innovative contributions is the alternative analytical representation of the concentration curves in a coordinate system which assumes the so-called equidistribution line as x-axis and its perpendicular line as y-axis. Furthermore, the impact of the presence of a superior and/or inferior limit in the variable of interest on the maximum concentration triangle is examined: suitable correction coefficients are derived for computing the corresponding concentration ratio, that take into account these restrictions.