The binomial decomposition of the single parameter family of GB welfare functions

We consider the binomial decomposition of generalized Gini welfare functions in terms of the binomial welfare functions Cj, j = 1,...,n and we examine the weighting structure of the binomial welfare functions Cj, j = 1,...,n which progressively focus on the poorest part of the population. We introduce a parametric family of income distributions and we illustrate the numerical behavior of the single parameter family of GB welfare functions with respect to those income distributions. Moreover, we investigate the binomial decomposition of the GB welfare functions and we illustrate the dependence of the binomial decomposition coefficients in relation with the single parameter which describes the family.