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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 2, Pages 223–237 (Mi tvp370)

Asymptotic Normality in a Classical Problem with Balls

B. A. Sevast'yanova, V. P. Čistyakovb

a Moscow
b Moscow

Abstract: Each of $n$ balls is deposited in a cell selected at random out of $N$ given cells.The probability of one cell being selected is equal to ${1/N}$, with the successive selections being mutually independent. Let $0\leqq r_1<r_2<…<r_s$ be arbitrary fixed integers. The symbol $\mu _r$ denotes a random variable representing the number of those cells that contain exactly $r$ balls. In [3] I. Weiss has proved the integral normal theorem for $\mu_0$ by the method of moments. In this paper we prove the local normal theorem for the random vector $(\mu _{r_1},…,\mu _{r_s})$ when $N$, $n\to\infty$ and $0<\alpha _0\leqslant n/{N \leqq\alpha_1}<\infty$ ($\alpha_0$, $\alpha_1$ are constants). In the proof we use the saddle-point method.

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English version:
Theory of Probability and its Applications, 1964, 9:2, 198–211

Bibliographic databases:

Citation: B. A. Sevast'yanov, V. P. Čistyakov, “Asymptotic Normality in a Classical Problem with Balls”, Teor. Veroyatnost. i Primenen., 9:2 (1964), 223–237; Theory Probab. Appl., 9:2 (1964), 198–211

Citation in format AMSBIB
\Bibitem{SevChi64} \by B.~A.~Sevast'yanov, V.~P.~{\v C}istyakov \paper Asymptotic Normality in a~Classical Problem with Balls \jour Teor. Veroyatnost. i Primenen. \yr 1964 \vol 9 \issue 2 \pages 223--237 \mathnet{http://mi.mathnet.ru/tvp370} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=166855} \zmath{https://zbmath.org/?q=an:0142.14704} \transl \jour Theory Probab. Appl. \yr 1964 \vol 9 \issue 2 \pages 198--211 \crossref{https://doi.org/10.1137/1109034} 

• http://mi.mathnet.ru/eng/tvp370
• http://mi.mathnet.ru/eng/tvp/v9/i2/p223

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Erratum
• Letter to the Editor
B. A. Sevast'yanov, V. P. Chistyakov
Teor. Veroyatnost. i Primenen., 1964, 9:3, 568
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