Distributive Compensation Ratio Derived from the Decomposition of the Mean Difference of a Sum
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In this paper a distributive compensation index, based on the decomposition of the mean difference of a sum Y of the k variates X1, … , Xi, … , Xk , has been proposed. The index takes value 0 if among the k variates there is no-compensation, which means that the k variates are uniformly ranked. The index is equal to 1 if among the k variates there is maximum compensation, which means that the sum X1 + … + Xi + … + Xk is constantly equal to the mean μ(Y). It has been also shown that if the k variates assume the integer values 1, 2, … , N, then the index is equal to: 1 – 3G(Y), where G(Y) is Gini’s concentration index evaluated on the sum.
Keywords: Mean difference, Uniform ranking, Co-graduation, Maximum Compensation, Compensation term, Compensation ratio. Author biographyMichele Zenga, Università di Milano-Biccocca, e-mail: michele.zenga@unimib.it. |
