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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:

Received: 05.03.1963

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}


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    Erratum
    • Letter to the Editor
      B. A. Sevast'yanov, V. P. Chistyakov
      Teor. Veroyatnost. i Primenen., 1964, 9:3, 568
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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