Idempotent copulae: Ordinal sums and Archimedean copula

Idempotent copulm have been characterised, in an implicit form, in [17]; here we look at a few well-known classes of copulas, namely, Frechet copulas, ordinal sums, Archimedean copulas, copulas of the type C(u, v) = uv +/- f(u)g(v) and a special subset of copulas represented through measure-preserving transformations, and characterise those among these classes that are idempotent. (C) 2016 Elsevier Inc. All rights reserved.