Stochastic Dominance and Moment Inequalities

For any distribution function (df) F, define F¹ = F and Fⁿ⁺¹ (x) = ∫_−∞^xFⁿ(y) dy. For two df's F and G, we obtain a relationship between the behaviour of Gⁿ(x) − Fⁿ(x) for large x and certain inequalities involving the moments of F and G. In particular, we generalize Fishburn's theorem, which deduces such inequalities from the condition that Gⁿ(x) − Fⁿ(x) ≥ 0 for all x.