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Abstract
Stochastic dominance orders of all finite degrees are defined on the set of distribution functions on the nonnegative real numbers in terms of integrals of the distributions. It is proved that if F strictly nth-degree stochastically dominates G, and if the moments of F and G through order n are finite with μFk = ∫Xk dF (x), then (μF1, …, μFn) ≠ (μG1, …, μGn) and (−1)k−1 μFk > (−1)k−1 μGk for the smallest k for which μFk ≠ μGk.
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