Asymptotic expansion of the power function of the two-sample binomial test with and without randomization

The paper deals with the asymptotic expansion of the power function of the two-sample binomial test. This test is a conditional test which is based upon the hypergeometric distribution, and we consider both the version with and without randomization. First, we give the asymptotic expansion of the hypergeometric distribution function and of its quantiles including randomization weights. Then we describe the asymptotic expansions of the power function of the two test versions and discuss the results.