Generalized Gini's mean difference through distortions and copulas, and related minimizing problems

07/26/2023

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by   Marco Capaldo, et al.

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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.