Copulas Constructed from Diagonal Sections

Fredricks, Gregory A.; Nelsen, Roger B.

doi:10.1007/978-94-011-5532-8_16

Cited by 42 publications

(22 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A diagonal is a function d : I-I with the properties (i) dð1Þ ¼ 1; (ii) dðtÞpt for all t in I; and (iii) 0pdðt 2 Þ À dðt 1 Þp2ðt 2 À t 1 Þ for all t 1 ; t 2 in I such that t 1 pt 2 : Note that the diagonal section of any quasi-copula (and thus any copula) is a diagonal, and for any diagonal d; there exist copulas (and thus quasi-copulas) whose diagonal section is d: For example (see [3,4] v À minðt À dðtÞjtA½v; uÞ; vpu: ð3:5Þ…”

Section: Copulas With Given Diagonal Sectionsmentioning

confidence: 98%

Best-possible bounds on sets of bivariate distribution functions

Nelsen

Molina

Rodrı́guez-Lallena

et al. 2004

Journal of Multivariate Analysis

View full text Add to dashboard Cite

The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fre´chet-Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G; respectively, then maxð0; F ðxÞ þ GðyÞ À 1ÞpHðx; yÞpminðF ðxÞ; GðyÞÞ for all x; y in ½ÀN; N: In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function H with given margins F and G when the values of H are known at quartiles of X and Y : r

show abstract

Section: Copulas With Given Diagonal Sectionsmentioning

confidence: 98%

Best-possible bounds on sets of bivariate distribution functions

Nelsen

Molina

Rodrı́guez-Lallena

et al. 2004

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…This construction is, hence, trivial in the case H is a copula and, hence, C = H. In all other cases, it may give several other copulas. When H(x, y) ≥ W (x, y) on I 2 , it reduces to the construction described by Durante et al (2007b), which includes the diagonal copulas given by Fredricks and Nelsen (1997).…”

Section: Copulas Derived From Suitable 2-increasing Functionsmentioning

confidence: 99%

A New Characterization of Bivariate Copulas

Durante

Jaworski

2010

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

show abstract

“…R defined by d A ðtÞ :¼ Aðt; tÞ. If d is the diagonal section of some copula, then it is known that the function defined on ½0; 1 2 by K d ðu; vÞ :¼ min u; v; dðuÞ þ dðvÞ 2 is a copula whose diagonal section is d (see [22,26] and, analogously,…”

Section: Generalized Diagonal Patchwork Copulasmentioning

confidence: 96%