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 and considered a family of its possible distortions, we define two new measures of distance between 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.
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