Dependence and Order in Families of Archimedean Copulas

Roger B. Nelsen

Journal of Multivariate Analysis, 1997, vol. 60, issue 1, 111-122

Abstract: The copula for a bivariate distribution functionH(x, y) with marginal distribution functionsF(x) andG(y) is the functionCdefined byH(x, y)=C(F(x), G(y)).Cis called Archimedean ifC(u, v)=[phi]-1([phi](u)+[phi](v)), where[phi]is a convex decreasing continuous function on (0, 1] with[phi](1)=0. A copula has lower tail dependence ifC(u, u)/uconverges to a constant[gamma]in (0, 1] asu-->0+; and has upper tail dependence ifC(u, u)/(1-u) converges to a constant[delta]in (0, 1] asu-->1-whereCdenotes the survival function corresponding toC. In this paper we develop methods for generating families of Archimedean copulas with arbitrary values of[gamma]and[delta], and present extensions to higher dimensions. We also investigate limiting cases and the concordance ordering of these families. In the process, we present answers to two open problems posed by Joe (1993,J. Multivariate Anal.46262-282).

Keywords: Archimedean; copula; bivariate; distribution; multivariate; distribution; concordance; ordering; lower; tail; dependence; upper; tail; dependence (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(96)91646-2
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:60:y:1997:i:1:p:111-122

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().