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On the construction of copulas and quasi-copulas with given diagonal sections
Authors:Roger B Nelsen  José Antonio Rodríguez-Lallena
Institution:a Department of Mathematical Sciences, Lewis & Clark College, 0615 S.W. Palatine Hill Road, Portland, OR 97219, USA
b Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
c Departamento de Estadística y Matemática Aplicada, Universidad de Almería, 04120 Almería, Spain
Abstract:We study a method, which we call a copula (or quasi-copula) diagonal splice, for creating new functions by joining portions of two copulas (or quasi-copulas) with a common diagonal section. The diagonal splice of two quasi-copulas is always a quasi-copula, and we find a necessary and sufficient condition for the diagonal splice of two copulas to be a copula. Applications of this method include the construction of absolutely continuous asymmetric copulas with a prescribed diagonal section, and determining the best-possible upper bound on the set of copulas with a particular type of diagonal section. Several examples illustrate our results.
Keywords:60E15  62E10  62H20
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