Edgeworth expansions with exact cumulants for two-sample linear rank statistics

We show how to compute exact cumulants of two-sample linear rank statistics In order to approximate tail-probabilities of these statistics, we consider Edgeworth expansions using these exact cumulants instead of asymptotic cumulants. Finally, we use exact tail probabilities to show that in several cases Edgeworth expansions with exact cumulants provides a significantly better approximation than other existing methods.