The exact region determined by Spearman's footrule, Gini's gamma and Kendall's tau
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918422680436736 |
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| author | Bukovšek, Damjana Kokol Lazić, Petra Mojškerc, Blaž Stopar, Nik |
| author_facet | Bukovšek, Damjana Kokol Lazić, Petra Mojškerc, Blaž Stopar, Nik |
| contents | Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall's tau, Gini's gamma and Spearman's footrule. In particular, we describe the exact region determined by these three measures, using shuffles of $M$ and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee's xi of ordinal sums of copulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07993 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The exact region determined by Spearman's footrule, Gini's gamma and Kendall's tau Bukovšek, Damjana Kokol Lazić, Petra Mojškerc, Blaž Stopar, Nik Statistics Theory 62H05, 62H20, 60E05 Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall's tau, Gini's gamma and Spearman's footrule. In particular, we describe the exact region determined by these three measures, using shuffles of $M$ and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee's xi of ordinal sums of copulas. |
| title | The exact region determined by Spearman's footrule, Gini's gamma and Kendall's tau |
| topic | Statistics Theory 62H05, 62H20, 60E05 |
| url | https://arxiv.org/abs/2601.07993 |