Extreme Copulas and the Comparison of Ordered Lists

B. Schuymer (), H. Meyer () and B. Baets ()

Theory and Decision, 2007, vol. 62, issue 3, 195-217

Abstract: We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T M (the minimum operator) and the Å\x81 ukasiewicz copula T L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T M and T L two probabilistic relations Q M and Q L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods. Copyright Springer Science+Business Media, LLC 2007

Keywords: comonotonic/countermonotonic comparison; copula; ordered list; probabilistic relation; transitivity (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s11238-006-9012-4 (text/html)
Access to full text is restricted to subscribers.

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:kap:theord:v:62:y:2007:i:3:p:195-217

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/11238/PS2

DOI: 10.1007/s11238-006-9012-4

Access Statistics for this article

Theory and Decision is currently edited by Mohammed Abdellaoui

More articles in Theory and Decision from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().