Stochastic Order (SO) Lehmann (1955) defines a random variable X to be stochastically larger than a random variable Y (denoted by X Y ) if F (a) ≤ G(a) for all a (with a strict inequality for some values of a), where F and G are the CDFs of X and Y , respectively.
if we observe a random value sampled from the first distribution, it is likely to be larger than a random value sampled from the second distribution.