Testing for Second-Order Stochastic Dominance of Two Distributions

A distribution function F is said to stochastically dominate another distribution function G in the second-order sense if , for all x. Second-order stochastic dominance plays an important role in economics, finance, and accounting. Here a statistical test has been constructed to test , for some x ∈ [a, b], against the hypothesis , for all x ∈ [a, b], where a and b are any two real numbers. The test has been shown to be consistent and has an upper bound α on the asymptotic size. The test is expected to have usefulness for comparison of random prospects for risk averters.