Measures of concordance determined by D4-invariant copulas
A continuous random vector (X,Y) uniquely determines a copula C:[0,1]2→[0,1] such that when the distribution functions of X and Y are properly composed into C, the joint distribution function of (X,Y) results. A copula is said to be D4-invariant if its mass distribution is invariant with respect to...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120440355X |
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| author | H. H. Edwards P. Mikusiński M. D. Taylor |
| author_facet | H. H. Edwards P. Mikusiński M. D. Taylor |
| author_sort | H. H. Edwards |
| collection | DOAJ |
| description | A continuous random vector (X,Y) uniquely determines a
copula C:[0,1]2→[0,1] such that when the distribution
functions of X and Y are properly composed into C, the
joint distribution function of (X,Y) results. A copula is
said to be D4-invariant if its mass distribution is
invariant with respect to the symmetries of the unit square.
A D4-invariant copula leads naturally to a family of
measures of concordance having a particular form, and all
copulas generating this family are D4-invariant. The
construction examined here includes Spearman’s rho and
Gini’s measure of association as special cases. |
| format | Article |
| id | doaj-art-ff6f970abe1c46619e2342ed35e77a6e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ff6f970abe1c46619e2342ed35e77a6e2025-02-03T05:45:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004703867387510.1155/S016117120440355XMeasures of concordance determined by D4-invariant copulasH. H. Edwards0P. Mikusiński1M. D. Taylor2Department of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USADepartment of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USADepartment of Mathematics, University of Central Florida, Orlando 32816-1364, FL, USAA continuous random vector (X,Y) uniquely determines a copula C:[0,1]2→[0,1] such that when the distribution functions of X and Y are properly composed into C, the joint distribution function of (X,Y) results. A copula is said to be D4-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. A D4-invariant copula leads naturally to a family of measures of concordance having a particular form, and all copulas generating this family are D4-invariant. The construction examined here includes Spearman’s rho and Gini’s measure of association as special cases.http://dx.doi.org/10.1155/S016117120440355X |
| spellingShingle | H. H. Edwards P. Mikusiński M. D. Taylor Measures of concordance determined by D4-invariant copulas International Journal of Mathematics and Mathematical Sciences |
| title | Measures of concordance determined by D4-invariant copulas |
| title_full | Measures of concordance determined by D4-invariant copulas |
| title_fullStr | Measures of concordance determined by D4-invariant copulas |
| title_full_unstemmed | Measures of concordance determined by D4-invariant copulas |
| title_short | Measures of concordance determined by D4-invariant copulas |
| title_sort | measures of concordance determined by d4 invariant copulas |
| url | http://dx.doi.org/10.1155/S016117120440355X |
| work_keys_str_mv | AT hhedwards measuresofconcordancedeterminedbyd4invariantcopulas AT pmikusinski measuresofconcordancedeterminedbyd4invariantcopulas AT mdtaylor measuresofconcordancedeterminedbyd4invariantcopulas |