2020/11/18 by Takaaki Koike, Marius Hofert, Koike, Takaaki +1
Decision Sciences · #62H10 #62H20 #FOS: Mathematics #Multi-Criteria Decision Making #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2011.09053
openalex publication_date 2020/11/18 · openalex created_date 2023/02/15 · openalex updated_date 2026/08/01
Representations of measures of concordance in terms of Pearson' s correlation coefficient are studied. All transforms of random variables are characterized such that the correlation coefficient of the transformed random variables is a measure of concordance. Next, Gini' s gamma is generalized and it is shown that the resulting generalized Gini' s gamma can be represented as a mixture of measures of concordance that are Pearson' s correlation coefficients of transformed random variables. As an application of this correlation mixture representation of generalized Gini' s gamma, lower and upper bounds of the compatible set of generalized Gini' s gamma, which is the collection of all possible square matrices whose entries are pairwise bivariate generalized Gini' s gammas, are derived.