However, 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.
we compute ε such that a value of 0 would mean that the noisy version is superior.