hypothesis of randomness; weak law of large numbers; randomized ranks; averaged scores
The author studies the linear rank statistics for testing the pypothesis of randomness against the alternative of two samples provided both are drawn grom discrete (integer-valued) distributions. The weak law of large numbers and the exact slope are obtained for statistics with randomized ranks of with averaged scores.
 J. Hájek: Asymptotic sufficiency of the vector of ranks in the Bahadur sense
. Ann. Statist. 2(1974), 1105-1125. MR 0356355
 D. Vorlíčková: Asymptotic properties of rank tests under discrete distributions
. Z. Wahrscheinlichkeitstheorie. verw. Geb. 14 (1970), 275-289. DOI 10.1007/BF00533666
| MR 0269049