location problem; $E$-test statistic; $M$-test statistic
Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s $E$-test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics.
 J. Hájek, Z. Šidák: Theory of rank tests
. Academic Press, Orlando, 1967. MR 0229351
 Z. Šidák: Tables for the two-sample location $E$-test based on exceeding observations
. Apl. Mat. 22 (1977), 166–175. MR 0440791
 Z. Šidák, J. Vondráček: A simple non-parametric test of the difference in location of two populations
. Apl. Mat. 2 (1957), 215–221. MR 0090203