Abstract
Aiming at the simplest possible representation of maxmin copulas in terms of two generators Košir and Omladič recently introduced the class of so-called reflected maxmin (RMM) copulas in [10]. All results for RMM copulas can easily be translated to results on maxmin copulas. Building upon the afore-mentioned article we provide alternative simplified (mainly Markov kernel based) proofs for some of their theorems and, more importantly, derive numerous new results. In particular, we show that the family of all RMM copulas is a compact subset of the metric space of all copulas (with the standard uniform metric), characterize absolutely continuous RMM copulas, and show that the limit of absolutely continuous RMM copulas is absolutely continuous too. Finally, we determine Kendall's τ and Spearman's ρ of RMM copulas, prove some first inequalities for τ and ρ, and state a conjecture on sharp inequalities. Some examples illustrating the main results round off the paper.
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