Kachapova, F; Kachapov, I
MetadataShow full metadata
Monotonicity 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.