RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2001, Volume 46, Issue 4, Pages 713–723 (Mi tvp3796)  

This article is cited in 7 scientific papers (total in 7 papers)

Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns

V. G. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Let $X_1,…,X_m$ and $Y_1,…,Y_n$ be two sequences of independent identically distributed random variables taking on values $1,2,…$ . By means of a particular version of the Stein method we construct an estimate of the accuracy of approximation for the distribution of the number of matching patterns of outcomes $X_i,…,X_{i+s-1}$ of a given length $s$ in the first sequence with the patterns of outcomes $Y_j,…,Y_{j+s-1}$ in the second sequence. The approximating distribution is the distribution of the sum of Poisson number of independent random variables with geometric distribution.

Keywords: long repetitions, coincidence of words, estimates of accuracy of the Poisson approximation, compound Poisson distribution, Stein method, Chen–Stein method.

DOI: https://doi.org/10.4213/tvp3796

Full text: PDF file (968 kB)

English version:
Theory of Probability and its Applications, 2002, 46:4, 667–675

Bibliographic databases:

Received: 29.12.1998
Revised: 05.07.1999

Citation: V. G. Mikhailov, “Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns”, Teor. Veroyatnost. i Primenen., 46:4 (2001), 713–723; Theory Probab. Appl., 46:4 (2002), 667–675

Citation in format AMSBIB
\Bibitem{Mik01}
\by V.~G.~Mikhailov
\paper Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns
\jour Teor. Veroyatnost. i Primenen.
\yr 2001
\vol 46
\issue 4
\pages 713--723
\mathnet{http://mi.mathnet.ru/tvp3796}
\crossref{https://doi.org/10.4213/tvp3796}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1971829}
\zmath{https://zbmath.org/?q=an:1040.60007}
\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 4
\pages 667--675
\crossref{https://doi.org/10.1137/S0040585X97979287}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000179604100007}


Linking options:
  • http://mi.mathnet.ru/eng/tvp3796
  • https://doi.org/10.4213/tvp3796
  • http://mi.mathnet.ru/eng/tvp/v46/i4/p713

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “On the asymptotic properties of the distribution of the number of pairs of $H$-connected chains”, Discrete Math. Appl., 12:4 (2002), 393–400  mathnet  crossref  mathscinet  zmath
    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. A. M. Shoitov, “The Poisson approximation for the number of matches of values of a discrete function from chains”, Discrete Math. Appl., 15:3 (2005), 241–254  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. 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
    5. V. G. Mikhailov, “A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences”, Theory Probab. Appl., 53:1 (2009), 106–116  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. M. Zubkov, V. I. Kruglov, “On coincidences of tuples in a binary tree with random labels of vertices”, Discrete Math. Appl., 26:3 (2016), 145–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. V. I. Kruglov, “On coincidences of tuples in a $q$-ary tree with random labels of vertices”, Discrete Math. Appl., 28:5 (2018), 293–307  mathnet  crossref  crossref  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:220
    Full text:42

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019