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On the characterization of a class of binary operations on bivariate distribution functions. (English) Zbl 1121.60010

Summary: We characterize the class of binary operations on bivariate distribution functions that are induced pointwise by a two-place real function (e.g. mixtures) and, in particular, we study these operations on the class of distribution functions whose one-dimensional margins are uniform (i.e. copula).

MSC:

60E05 Probability distributions: general theory
60B10 Convergence of probability measures
62E10 Characterization and structure theory of statistical distributions
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