Osservazioni sull'indice di compensazione distributiva

Recently Zenga has proposed a normalized compensation index based on a decomposition of the mean difference of the sum Y of the k variates X1, ..., Xk. This paper proposes a decomposition of the above index to evaluate the percent contribution of a generic variate Xj to compensation. Moreover, the importance of a comparison between the observed value of the index and its value under the hypothesis of distributive independence is emphasized, to understand exhaustively the concept of compensation. The index's capability of measuring compensation of a complex phenomena, possibly composed by a number of different elements, is shown by a numerical example and by two applications to real data (a sample survey of total income of Italian families in 2001 and a dataset concerning marks of graduate students of Milano-Bicocca University in four exams).