In such cases we would not want to determine that X ∼ F is stochastically dominant over Y ∼ G because its CDF is strictly above the CDF of Y , and hence Y is stochastically larger than X.
according to this relaxation, X ∼ F is indeed stochastically larger than Y ∼ G. Almost Stochastic Dominance To overcome the limitations of the above straight forward approach, and define a relaxation of stochastic order, we turn to a definition that is based on the proportion of points in the domain of the participating distributions for which SO holds.