Abstract:
We study the number distribution for monotone strings of a length $s$ in a sequence of $n$ random independent variables uniformly distributed on the set $\{0,\dots,N-1\}$ where $N$ is a constant. By means of the Stein method we construct an estimate of the variation distance between this distribution and a compound Poisson distribution. As a corollary of this result we prove the limit theorem as $n,s\to\infty$ for the number of monotone strings. The approximating distribution is the distribution of the sum of Poisson number of independent random variables with geometric distribution.
Keywords:
monotone strings, estimate of the variation distance of the compound Poisson approximation, compound Poisson distribution, Stein method.
Bibliographic databases:
Document Type:
Article
UDC:519.214
Language: Russian
Citation:
A. A. Minakov, “Compound Poisson approximation of the number distribution for monotone strings of fixed length in a random sequence”, Prikl. Diskr. Mat., 2015, no. 2(28), 21–29
\Bibitem{Min15}
\by A.~A.~Minakov
\paper Compound Poisson approximation of the number distribution for monotone strings of fixed length in a~random sequence
\jour Prikl. Diskr. Mat.
\yr 2015
\issue 2(28)
\pages 21--29
\mathnet{http://mi.mathnet.ru/pdm507}
\crossref{https://doi.org/10.17223/20710410/28/2}
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https://www.mathnet.ru/eng/pdm507
https://www.mathnet.ru/eng/pdm/y2015/i2/p21
This publication is cited in the following 3 articles:
V. Čekanavičius, S. Y. Novak, “Compound Poisson approximation”, Probab. Surveys, 19:none (2022)
S. Y. Novak, “Poisson approximation”, Probab. Surveys, 16:none (2019)
A. A. Minakov, “Poisson approximation for the number of non-decreasing runs in Markov chains”, Matem. vopr. kriptogr., 9:2 (2018), 103–116
Citation in format AMSBIB
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