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

Marco Capaldo, Antonio Di Crescenzo and Franco Pellerey

Statistics & Probability Letters, 2024, vol. 206, issue C

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.

Keywords: Distance metrics; Distortion function; Copula; Proportional hazard model; Proportional reversed hazard model; Gini’s mean difference (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.109981

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