Dependence and Order in Families of Archimedean Copulas
The copula for a bivariate distribution functionH(x,Â y) with marginal distribution functionsF(x) andG(y) is the functionCdefined byH(x,Â y)=C(F(x),Â G(y)).Cis called Archimedean ifC(u,Â v)=[phi]-1([phi](u)+[phi](v)), where[phi]is a convex decreasing continuous function on (0,Â 1] with[phi](1)=0. A copula has lower tail dependence ifC(u,Â u)/uconverges to a constant[gamma]in (0,Â 1] asu-->0+; and has upper tail dependence ifC(u,Â u)/(1-u) converges to a constant[delta]in (0,Â 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).
Volume (Year): 60 (1997)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:111-122. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.