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Teoriya Veroyatnostei i ee Primeneniya, 1982, Volume 27, Issue 3, Pages 599–606
(Mi tvp2396)
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This article is cited in 13 scientific papers (total in 13 papers)
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 $X_1,\dots,X_n$ 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
$$
\mathbf P\{V_n(t)<h(t)\ \forall t\colon 0<F(t)<1\}
$$
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.
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
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https://www.mathnet.ru/eng/tvp2396 https://www.mathnet.ru/eng/tvp/v27/i3/p599
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