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Teor. Veroyatnost. i Primenen., 1982, Volume 27, Issue 3, Pages 599–606 (Mi tvp2396)  

Short Communications

On the computation of the probability of noncrossing of the curve bound by the empirical process

V. F. Kotel'nikova, E. V. Hmaladze

Moscow

Abstract: Let $X_1,…,X_n$ 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
$$ \mathbf P\{V_n(t)<h(t) \forall t\colon 0<F(t)<1\} $$
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.

Full text: PDF file (633 kB)

English version:
Theory of Probability and its Applications, 1983, 27:3, 640–648

Bibliographic databases:

Received: 04.07.1980

Citation: V. F. Kotel'nikova, E. V. Hmaladze, “On the computation of the probability of noncrossing of the curve bound by the empirical process”, Teor. Veroyatnost. i Primenen., 27:3 (1982), 599–606; Theory Probab. Appl., 27:3 (1983), 640–648

Citation in format AMSBIB
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\by V.~F.~Kotel'nikova, E.~V.~Hmaladze
\paper On the computation of the probability of noncrossing of the curve bound by the empirical process
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 3
\pages 599--606
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=673936}
\zmath{https://zbmath.org/?q=an:0516.62050|0494.62023}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 3
\pages 640--648
\crossref{https://doi.org/10.1137/1127075}
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