The Bertino family of copulas. (English) Zbl 1135.62334

Fredricks, Gregory A.; Nelsen, Roger B.

Cuadras, Carles M. (ed.) et al., Distributions with given marginals and statistical modelling. Papers presented at the meeting, Barcelona, Spain, July 17–20, 2000. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0914-3/hbk). 81-91 (2002).

Summary: In this paper we present some of the salient properties of the Bertino family of copulas. We describe the support set of a Bertino copula and show that every Bertino copula is singular. We characterize Bertino copulas in terms of the joint distribution of max(\(U\), \(V\)) and min(\(U\), \(V\)) when \(U\) and \(V\) are uniform [0, 1] random variables whose copula is a Bertino copula. Finally, we find necessary and sufficient conditions for a Bertino copula to be extremal.
For the entire collection see [Zbl 1054.62002].

MSC:

62H05	Characterization and structure theory for multivariate probability distributions; copulas
62H20	Measures of association (correlation, canonical correlation, etc.)