On the Link Between the Concepts of Kurtosis and Bipolarization

In a paper on the measurement of the flatness of an income distribution Berrebi and Silber (1989) showed how it was possible to derive from the Gini index a measure of the degree of Kurtosis of a distribution whose definition made it quite similar to the more famous Pearson measure of Kurtosis. This note shows that it is possible to derive from the index of flatness proposed by Berrebi and Silber (1989) a measure of bipolarization that has all the important properties one would like a bipolarization index to have.