Gini's mean difference in the theory and application to inflated distributions

Abstract

In the paper we give interesting properties of Gini's mean difference. We thoroughly consider the appropriate literature taking account of book publications and articles. It constitutes an important complement to the extensive bibliography of papers based on Gini's ideas, presented by G.M. Giorgi in 1990. We show an application of the mean difference to inflated distributions which are of weight and interest in statistical problems.