English

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

Probability 2023-10-09 v2 Statistics Theory Statistics Theory

Abstract

Given a random variable XX and considered a family of its possible distortions, we define two new measures of distance between XX 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

Cite

@article{arxiv.2307.14307,
  title  = {Generalized Gini's mean difference through distortions and copulas, and related minimizing problems},
  author = {Marco Capaldo and Antonio Di Crescenzo and Franco Pellerey},
  journal= {arXiv preprint arXiv:2307.14307},
  year   = {2023}
}

Comments

14 pages, 3 figures, previous version submitted for publication on March 20, 2023

R2 v1 2026-06-28T11:40:54.690Z