Archivio Istituzionale della RicercaGiven a random variable X and considered a family of its possible distortions, we dfinee 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.
Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems / Capaldo, Marco; Di Crescenzo, Antonio; Pellerey, Franco. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - ELETTRONICO. - 206:(2024), pp. 1-12. [10.1016/j.spl.2023.109981]
Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems
Franco Pellerey
2024
Abstract
Given a random variable X and considered a family of its possible distortions, we dfinee 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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Generalized GMD.pdf
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https://hdl.handle.net/11583/2984082