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

 Teor. Veroyatnost. i Primenen., 1976, Volume 21, Issue 1, Pages 190–195 (Mi tvp3315)

Short Communications

Asymptotic normality of one class of statistics in a multinomial scheme

G. I. Ivčenko, V. V. Levin

Moscow

Abstract: There are $N$ cells into which $n_j$ particles of the $j$-th type are thrown independently of each other, $j=1,…,s$. Particles of the $j$-th type are distributed in cells with the probabilities $p_{1j},…,p_{Nj}$. Let
$$L_r=\sum_{m=1}^N f_{mr}^{(N)}(\nu_{m1},…,\nu_{ms}),$$
where $\nu_{mj}$ is the number of particles of the $j$-th type in the $m$-th cell and $f_{mr}^{(N)}(x_1,…,x_s)$ are some given functions. The central limit theorem for the multidimensional random variables $(L_1,…,L_k)$, as $N,n_1,…,n_s\to\infty$, is proved.

Full text: PDF file (399 kB)

English version:
Theory of Probability and its Applications, 1976, 21:1, 188–192

Bibliographic databases:

Citation: G. I. Ivčenko, V. V. Levin, “Asymptotic normality of one class of statistics in a multinomial scheme”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 190–195; Theory Probab. Appl., 21:1 (1976), 188–192

Citation in format AMSBIB
\Bibitem{IvcLev76} \by G.~I.~Iv{\v{c}}enko, V.~V.~Levin \paper Asymptotic normality of one class of statistics in a~multinomial scheme \jour Teor. Veroyatnost. i Primenen. \yr 1976 \vol 21 \issue 1 \pages 190--195 \mathnet{http://mi.mathnet.ru/tvp3315} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=410856} \zmath{https://zbmath.org/?q=an:0392.62016} \transl \jour Theory Probab. Appl. \yr 1976 \vol 21 \issue 1 \pages 188--192 \crossref{https://doi.org/10.1137/1121021} 

• http://mi.mathnet.ru/eng/tvp3315
• http://mi.mathnet.ru/eng/tvp/v21/i1/p190

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. I. Ivchenko, O. V. Polepchuk, S. A. Khonov, “Concerning a class of similarity tests”, Math. Notes, 58:4 (1995), 1049–1056