The binomial decomposition of generalized Gini welfare functions, the S-Gini and Lorenzen cases

We consider the binomial decomposition of generalized Gini welfare functions in terms of the binomial welfare functions and the associated binomial inequality indices. We examine in detail the weights of the binomial welfare functions and the coefficients of the associated binomial inequality indices which progressively focus on the poorest sector of the population, and we illustrate the numerical behavior of the binomial welfare functions and inequality indices in relation with a new parametric family of income distributions. The main contribution of the paper is to investigate the analogy between the binomial welfare functions and the S-Gini and Lorenzen parametric families of generalized Gini welfare functions, particularly in the context of the binomial decomposition. Finally, we examine the orness of the parametric S-Gini and Lorenzen families of generalized Gini welfare functions.