Four Measures of Association and Their Representations in Terms of Copulas
Four measures of association, namely, Spearman’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>, Kendall’s <inline-formula><math x...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/4/1/19 |
| _version_ | 1827307237292376064 |
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| author | Michel Adès Serge B. Provost Yishan Zang |
| author_facet | Michel Adès Serge B. Provost Yishan Zang |
| author_sort | Michel Adès |
| collection | DOAJ |
| description | Four measures of association, namely, Spearman’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>, Kendall’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, Blomqvist’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> and Hoeffding’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>2</mn></msup></semantics></math></inline-formula>, are expressed in terms of copulas. Conveniently, this article also includes explicit expressions for their empirical counterparts. Moreover, copula representations of the four coefficients are provided for the multivariate case, and several specific applications are pointed out. Additionally, a numerical study is presented with a view to illustrating the types of relationships that each of the measures of association can detect. |
| first_indexed | 2024-04-24T18:36:54Z |
| format | Article |
| id | doaj.art-99020395016f490daf145ee407dc26c6 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-04-24T18:36:54Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-99020395016f490daf145ee407dc26c62024-03-27T13:18:51ZengMDPI AGAppliedMath2673-99092024-03-014136338210.3390/appliedmath4010019Four Measures of Association and Their Representations in Terms of CopulasMichel Adès0Serge B. Provost1Yishan Zang2Département de Mathématiques, Université du Québec à Montréal, Montréal, QC H2X 3Y7, CanadaDepartment of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, CanadaDepartment of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, CanadaFour measures of association, namely, Spearman’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>, Kendall’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, Blomqvist’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> and Hoeffding’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>2</mn></msup></semantics></math></inline-formula>, are expressed in terms of copulas. Conveniently, this article also includes explicit expressions for their empirical counterparts. Moreover, copula representations of the four coefficients are provided for the multivariate case, and several specific applications are pointed out. Additionally, a numerical study is presented with a view to illustrating the types of relationships that each of the measures of association can detect.https://www.mdpi.com/2673-9909/4/1/19Blomqvist’s correlation coefficientcopulasHoeffding’s dependence indexKendall’s rank correlation coefficientmultivariate measures of dependenceSpearman’s rank correlation |
| spellingShingle | Michel Adès Serge B. Provost Yishan Zang Four Measures of Association and Their Representations in Terms of Copulas AppliedMath Blomqvist’s correlation coefficient copulas Hoeffding’s dependence index Kendall’s rank correlation coefficient multivariate measures of dependence Spearman’s rank correlation |
| title | Four Measures of Association and Their Representations in Terms of Copulas |
| title_full | Four Measures of Association and Their Representations in Terms of Copulas |
| title_fullStr | Four Measures of Association and Their Representations in Terms of Copulas |
| title_full_unstemmed | Four Measures of Association and Their Representations in Terms of Copulas |
| title_short | Four Measures of Association and Their Representations in Terms of Copulas |
| title_sort | four measures of association and their representations in terms of copulas |
| topic | Blomqvist’s correlation coefficient copulas Hoeffding’s dependence index Kendall’s rank correlation coefficient multivariate measures of dependence Spearman’s rank correlation |
| url | https://www.mdpi.com/2673-9909/4/1/19 |
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