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two sample problem; rank order statistics; simple random walk; exact distributions
The distributions of rank order statistics are studied for the case of arbitrary sample sizes in the two sample problem. The method applied is a generalization of Dwass's method from his paper in Ann. Math. Statist. 38 (1967), based on the analogy of rank order statistics and functions on a simple random walk.
[1] M. Dwass: Simple random walk and rank order statistics. Ann. Math. Statist. 38 (1967), 1042-1053. DOI 10.1214/aoms/1177698773 | MR 0215463 | Zbl 0162.50204
[2] W. Feller: An introduction to probability theory and its applications. 2nd edition. J. Wiley, New York 1967. MR 0243559 | Zbl 0158.34902
[3] S. G. Mohanty B. R. Handa: Rank order statistics related to a generalized random walk. Studia Sci. Math. Hung. 5 (1970), 267-276. MR 0295488
[4] J. Reimann I. Vincze: On the comparison of two samples with slightly different sizes. A Magyar Tud. Akad. matem. Kutató Intezetének Közleményei 5 (1960), 293-300. MR 0132649
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