Is it possible to assign a given curve of monofunction on [0;1] to be a support of a copula (or copulas)?

29 June 2020 0 2K Report

Nelsen, in his famous book "Introduction to copulas", gave via examples (see paragraph 3.2.1) a way to construct copulas with prescibed support. He treated the case of segments and arcs of circles.

Now, if a given function f: [0;1]\rightarrow [0:a] is a continuous and if we denote its curve by C_f, is it possible to construct a copula with support C_f. If not (that's more likely), what are classes of such functions that verify the desired property?

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