Kachapova, FKachapov, I2013-06-072013-06-0720132013International conference on probability and statistics , Dubai, 2013-01-30, published in: World Academy of Science, Engineering and Technology (73), pp.1594 - 15992010-376X2010-3778https://hdl.handle.net/10292/5434Monotonicity is an important type of dependence of random variables. The paper reviews the definitions of comonotonicity and counter-monotonicity, their existing criteria and introduces a new criterion for each of the two concepts, along with some proofs. The new criteria are similar to the definition of a monotone function and clarify the meaning of the monotonicity concept. Stronger criteria are proven for the case of continuous marginals.World Academy of Science, Engineering and Technology is a scholarly open access, peer reviewed, interdisciplinary, monthly and fully refereed international journal focusing on theories, methods and applications in Science, Engineering and Technology.ComonotonicCounter-monotonicMarginalMonotonicityConference ContributionOpenAccess