Abstract
We provide necessary and sufficient conditions on a function f:[0,1]→R+ so that Hf(C)(u,v)=C(u,v)f(1−u−v+C(u,v)), (u,v)∈[0,1]2 is a copula for any bivariate copula C. Then we discuss several important bivariate copula properties preserved or not by the mapping C↦Hf(C). The considered bivariate copula construction unifies many examples found in the literature and opens a qualitatively new way of obtaining new copulas by simply using a function f which has to satisfy a few easily verifiable properties.
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