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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 1, Pages 128–135
(Mi tvp3280)
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This article is cited in 2 scientific papers (total in 2 papers)
Short Communications
Some remarks on summing independent variables in the non-classical case
V. I. Rotar' Moscow
Abstract:
Let $\{F_{jn}\}_{j=1}^n$ and $\{G_{jn}\}_{j=1}^n$ be two triangular arrays of distribution functions. Let $b_n$ be such that
$$
\sum_{j=1}^nb_n^{-2}\int_0^{b_n}x[1-F_{jn}(x)+F_{jn}(-x)]\,dx=\delta/n,
$$
where $0<\delta\le 1$;
$$
a_{jn}=\int_{-b_n}^{b_n}x\,dF_{jn}(x),\qquad a'_{jn}=\int_{-b_n}^{b_n}x\,dG_{jn}(x).
$$
The paper deals with conditions under which
$$
*\hskip-4,5mm\prod_{j=1}^nF_{jn}(xb_n+a_{jn})-{}{*\hskip-4,5mm}\prod_{j=1}^nG_{jn}(xb_n+a'_{jn})\to 0
$$
weakly with respect to the classes $C$ or $C_0$.
Received: 31.10.1974
Citation:
V. I. Rotar', “Some remarks on summing independent variables in the non-classical case”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 128–135; Theory Probab. Appl., 21:1 (1976), 130–137
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https://www.mathnet.ru/eng/tvp3280 https://www.mathnet.ru/eng/tvp/v21/i1/p128
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