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Diskr. Mat., 2002, Volume 14, Issue 1, Pages 82–98 (Mi dm233)  

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

Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays

A. M. Shoitov


Abstract: In this paper we study random variables which characterise collections of segments in an equiprobable polynomial scheme related by the $H$-equivalence. We give an upper bound for the variation distance between the distribution of the random variable $\xi_k(H)$ equal to the number of collections of $H$-equivalent segments and the Poisson distribution. We present sufficient conditions for the convergence of the distribution functions of the number of $H$-equivalent segments in the triangular array scheme of equiprobable polynomial trials to the normal law, the Poisson law, and the compound Poisson law.

DOI: https://doi.org/10.4213/dm233

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English version:
Discrete Mathematics and Applications, 2002, 12:2, 165–181

Bibliographic databases:

UDC: 519.2
Received: 02.07.2001

Citation: A. M. Shoitov, “Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays”, Diskr. Mat., 14:1 (2002), 82–98; Discrete Math. Appl., 12:2 (2002), 165–181

Citation in format AMSBIB
\Bibitem{Sho02}
\by A.~M.~Shoitov
\paper Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays
\jour Diskr. Mat.
\yr 2002
\vol 14
\issue 1
\pages 82--98
\mathnet{http://mi.mathnet.ru/dm233}
\crossref{https://doi.org/10.4213/dm233}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1919858}
\zmath{https://zbmath.org/?q=an:1054.60006}
\transl
\jour Discrete Math. Appl.
\yr 2002
\vol 12
\issue 2
\pages 165--181


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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. 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
    2. A. M. Shoitov, “The compound Poisson distribution of the number of matches of values of a discrete function of $s$-tuples in segments of a sequence of random variables”, Discrete Math. Appl., 17:3 (2007), 209–230  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. A. M. Shoitov, “Strukturno ekvivalentnye tsepochki v ravnoveroyatnoi polinomialnoi skheme”, Matem. vopr. kriptogr., 3:3 (2012), 129–151  mathnet  crossref
  • Дискретная математика
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