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

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  • Capaldo, Marco
  • Di Crescenzo, Antonio
  • Pellerey, Franco

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.

Suggested Citation

  • Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002055
    DOI: 10.1016/j.spl.2023.109981
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    References listed on IDEAS

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