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Teor. Veroyatnost. i Primenen., 1974, Volume 19, Issue 4, Pages 855–864 (Mi tvp3990)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme

V. F. Kolchina, V. P. Chistyakov

a Moscow

Abstract: Let $\mu_0(s,n,p_1…,p_N)$ be the number of not appeared $s$-tuples in a sequence of $n+s-1$ independent trials, at each trial the probability of event $i$ being $p_i$, $i=1,…,N$.
We consider asymptotic behaviour of $\mu_0(s,n,p_1…,p_N)$ as $n,N$ and $n/N\to\infty$.
In particular, we obtain conditions under which the distributions of $\mu_0(s,n,p_1…,p_N)$ converge to a Poisson distribution without assuming $p_1…,p_N$ to be close to $1/N$.

Full text: PDF file (1265 kB)

English version:
Theory of Probability and its Applications, 1975, 19:4, 822–830

Bibliographic databases:

Received: 11.08.1974

Citation: V. F. Kolchin, V. P. Chistyakov, “Limit distributions of the number of not appeared $s$-tuples in a multinomial scheme”, Teor. Veroyatnost. i Primenen., 19:4 (1974), 855–864; Theory Probab. Appl., 19:4 (1975), 822–830

Citation in format AMSBIB
\Bibitem{KolChi74}
\by V.~F.~Kolchin, V.~P.~Chistyakov
\paper Limit distributions of the number of not appeared $s$-tuples in a~multinomial scheme
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 4
\pages 855--864
\mathnet{http://mi.mathnet.ru/tvp3990}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0370698}
\zmath{https://zbmath.org/?q=an:0323.60009}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 4
\pages 822--830
\crossref{https://doi.org/10.1137/1119093}


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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. A. M. Zubkov, “Inequalities for transition probabilities with taboos and their applications”, Math. USSR-Sb., 37:4 (1980), 451–488  mathnet  crossref  mathscinet  zmath  isi
    2. V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of $s$-tuples in random discrete sequences”, Discrete Math. Appl., 13:6 (2003), 541–568  mathnet  crossref  crossref  mathscinet  zmath
    3. N. M. Mezhennaya, “O chisle sovpadenii znakov v diskretnoi sluchainoi posledovatelnosti, upravlyaemoi tsepyu Markova”, Sib. elektron. matem. izv., 13 (2016), 305–317  mathnet  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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