Monotonicity properties of multivariate distribution and survival functions -- With an application to Lévy-frailty copulas

Paul Ressel

Journal of Multivariate Analysis, 2011, vol. 102, issue 3, 393-404

Abstract: The monotonicity properties of multivariate distribution functions are definitely more complicated than in the univariate case. We show that they fit perfectly well into the general theory of completely monotone and alternating functions on abelian semigroups. This allows us to prove a correspondence theorem which generalizes the classical version in two respects: the function in question may be defined on rather arbitrary product sets in , and it need not be grounded, i.e. disappear at the lower-left boundary. In 2009 a greatly interesting class of copulas was discovered by Mai and Scherer (cf. Mai and Scherer (2009) [4]), connecting in a very surprising way complete monotonicity with respect to the maximum operation on and with respect to ordinary addition on . Based on the preceding results, we give another proof of this result.

Keywords: Multivariate; distribution; function; Multivariate; survival; function; Completely; monotone; Completely; alternating; n-increasing; Fully; n-increasing; n-max-increasing; Correspondence; theorem; Levy-frailty; copula (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00207-1
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:102:y:2011:i:3:p:393-404

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 ().