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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{PDM_2015_2_a1,
     author = {A. A. Minakov},
     title = {Compound {Poisson} approximation of the number distribution for monotone strings of fixed length in a~random sequence},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {21--29},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_2_a1/}
}
TY  - JOUR
AU  - A. A. Minakov
TI  - Compound Poisson approximation of the number distribution for monotone strings of fixed length in a~random sequence
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 21
EP  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_2_a1/
LA  - ru
ID  - PDM_2015_2_a1
ER  - 
%0 Journal Article
%A A. A. Minakov
%T Compound Poisson approximation of the number distribution for monotone strings of fixed length in a~random sequence
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 21-29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_2_a1/
%G ru
%F PDM_2015_2_a1
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/