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On copulas and their diagonals. (English) Zbl 1171.62332
Summary: We formulate necessary and sufficient conditions for a function \(\delta :[0,1]\rightarrow [0,1]\) to be the diagonal section of a multivariate absolutely continuous copula. Moreover we provide some simple analytic formulas for copulas having given diagonal sections or given distribution functions of order statistics.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G30 Order statistics; empirical distribution functions
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