Integral generators of Archimedean n-copulas

Włodzimierz Wysocki

Journal of Nonparametric Statistics, 2019, vol. 31, issue 3, 629-662

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.

Date: 2019
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DOI: 10.1080/10485252.2019.1626382

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