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On the construction of copulas and quasi-copulas with given diagonal sections. (English) Zbl 1152.60311
Summary: 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.

MSC:
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions
62H20 Measures of association (correlation, canonical correlation, etc.)
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