Generalized Gini's mean difference through distortions and copulas, and related minimizing problems
share
Given a random variable X and considered a family of its possible distortions, we define two new measures of distance between X and each its distortion. For these distance measures, which are extensions of the Gini's mean difference, conditions are determined for the existence of a minimum, or a maximum, within specific families of distortions, generalizing some results presented in the recent literature.
READ FULL TEXT