Geodesic
Compound Poisson approximation of the number distribution for monotone strings of fixed length in a~random sequence
Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 21-29.

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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. 
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     author = {A. A. Minakov},
     title = {Compound {Poisson} approximation of the number distribution for monotone strings of fixed length in a~random sequence},
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     url = {http://geodesic.mathdoc.fr/item/PDM_2015_2_a1/}
}
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A. A. Minakov. Compound Poisson approximation of the number distribution for monotone strings of fixed length in a~random sequence. Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 21-29. http://geodesic.mathdoc.fr/item/PDM_2015_2_a1/

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