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On the \(\alpha \)-migrativity of semicopulas, quasi-copulas, and copulas. (English) Zbl 1191.62096

Summary: We address the problem of \(\alpha \)-migrativity (for a fixed \(\alpha \)) for semicopulas, copulas and quasi-copulas. We introduce the concept of an \(\alpha \)-sum of semicopulas. This new concept allows us to completely characterize \(\alpha \)-migrative semicopulas and copulas. Moreover, \(\alpha \)-sums also provide a means to obtain a partial characterization of \(\alpha \)-migrative quasi-copulas.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
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