# Copula–Induced Measures of Concordance

Dependence Modeling (2016)

- Volume: 4, Issue: 1, page 205-214, electronic only
- ISSN: 2300-2298

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topSebastian Fuchs. "Copula–Induced Measures of Concordance." Dependence Modeling 4.1 (2016): 205-214, electronic only. <http://eudml.org/doc/287103>.

@article{SebastianFuchs2016,

abstract = {We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas. We present conditions on ψΛ and on A under which these maps are measures of concordance. The resulting class of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’s gamma.},

author = {Sebastian Fuchs},

journal = {Dependence Modeling},

keywords = {copulas; transformations of copulas; measures of concordance},

language = {eng},

number = {1},

pages = {205-214, electronic only},

title = {Copula–Induced Measures of Concordance},

url = {http://eudml.org/doc/287103},

volume = {4},

year = {2016},

}

TY - JOUR

AU - Sebastian Fuchs

TI - Copula–Induced Measures of Concordance

JO - Dependence Modeling

PY - 2016

VL - 4

IS - 1

SP - 205

EP - 214, electronic only

AB - We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas. We present conditions on ψΛ and on A under which these maps are measures of concordance. The resulting class of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’s gamma.

LA - eng

KW - copulas; transformations of copulas; measures of concordance

UR - http://eudml.org/doc/287103

ER -

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