A look at the structure of some extended Ginis

摘要

This survey describes the structure of linear inequality measures especially of the Gini family including P- and M-measures and the indices of Bonferroni and De Vergottini. Different representations, relations and interpretations are described. The new tools P(k)- and M(k)-curves allow for a graphical interpretation of several problems. Generalized Glasser inequalities are derived, all including upper bounds with the coefficient of variation. Starting with well-known distribution functions as the Lorenz curve, the Bonferroni curve, the newly introduced transformed De Vergottini curve and others, the corresponding moments depend all on P -measures. Regression coefficients of different curves used in the measurement of inequality depend on extended Ginis.