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

Marco Capaldo; Antonio Di Crescenzo; Franco Pellerey

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arXiv · 2307.14307

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

Marco Capaldo·Antonio Di Crescenzo·Franco Pellerey

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Abstract

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.

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Marco Capaldo, Antonio Di Crescenzo, Franco Pellerey. 2023-07-26. Generalized Gini's mean difference through distortions and copulas, and related minimizing problems. https://arxiv.org/abs/2307.14307

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