Detecting complete and joint mixability

We introduce the Mixability Detection Procedure (MDP) to check whether a set of d distri- bution functions is jointly mixable at a given confidence level. The procedure is based on newly established results regarding the convergence rate of the minimal variance problem within the class of joint distribution functions with given marginals. The MDP is able to detect the complete mixability of an arbitrary set of distributions, even in those cases not covered by theoretical results. Stress-tests against borderline cases show that the MDP is fast and reliable.