|
Teoriya Veroyatnostei i ee Primeneniya, 1964, Volume 9, Issue 2, Pages 223–237
(Mi tvp370)
|
|
|
|
This article is cited in 33 scientific papers (total in 33 papers)
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 $0\leqq r_1<r_2<\dots<r_s$ 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 $(\mu _{r_1},\dots,\mu _{r_s})$ 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.
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
Linking options:
https://www.mathnet.ru/eng/tvp370 https://www.mathnet.ru/eng/tvp/v9/i2/p223
|
Statistics & downloads: |
Abstract page: | 330 | Full-text PDF : | 196 | First page: | 5 |
|