Geodesic
On the computation of the probability of noncrossing of the curve bound by the empirical process
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 599-606

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Let $X_1,\dots,X_n$ be independent random variables with continuous distribution function $F(x)$, $$ F_n(t)=n^{-1}\sum_{i=1}^nI(t-X_i) $$ be an associated empirical distribution function and $V_n(t)$ be an empirical process: $$ V_n(t)=\sqrt n[F_n(t)-F(t)]. $$ In the paper the recurrent formula (5) for the probabilities $$ \mathbf P\{V_n(t)(t)\ \forall t\colon 0(t)1\} $$ is given, where the function $h(t)$ supposed to be right-continuous. We use this formula for the computation of distribution functions of weighted Smirnov's statistics for a finite sample sizes (formulas (2) and (3)). The tables of percentage points of these distributions are given and a comparison with earlier results is made. 
@article{TVP_1982_27_3_a21,
     author = {V. F. Kotel'nikova and E. V. Hmaladze},
     title = {On the computation of the probability of noncrossing of the curve bound by the empirical process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {599--606},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a21/}
}
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V. F. Kotel'nikova; E. V. Hmaladze. On the computation of the probability of noncrossing of the curve bound by the empirical process. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 599-606. http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a21/