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

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

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

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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
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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, “On the asymptotic properties of the distribution of the number of pairs of $H$-connected chains”, Discrete Math. Appl., 12:4 (2002), 393–400
2. V. G. Mikhailov, A. M. Shoitov, “Structural equivalence of $s$-tuples in random discrete sequences”, Discrete Math. Appl., 13:6 (2003), 541–568
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
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
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
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
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
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