Integral generators of Archimedean n-copulas. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Wysocki, Włodzimierz
• Is Part Of: Journal of nonparametric statistics. Volume 31:Issue 3(2019)
• Page Start: 629
• Page End: 662
• Publication Date: 2019-07-03
• Subjects: Archimedean n-copula -- induced algebraic structure -- integral generator; 62H20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2019.1626382
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: We introduce two algebraic structures induced by an Archimedean n -copula: a one-parameter group of transformations and a one-parameter local group of transformations. We then study the natural functional characteristics (integral generators) of these structures. We discuss differential equations joining the integral generators and the additive generators of copulas. We show that the algebraic structures can be recovered by using a certain parametric family of differential equations. Finally, we give some applications of integral generators, and we indicate potential applications of the algebraic and analytical results obtained.