Geodesic
Compound Poisson approximation for the distribution of the number of monotone tuples in random sequence
Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 29-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The distribution of the number of monotone tuples in the sequence of independent uniformly distributed random variables taking values in the set $\{0,\dots ,N-1\}$ is considered. By means of the Stein method, an estimate for the variation distance between the distribution of the number of monotone tuples and compound Poisson distribution are constructed. As a corollary of this result, the limit theorem for the number of monotone tuples is proved. The approximating distribution in it is the distribution of the sum of Poisson number of independent random variables with geometric distribution.
Mots-clés : monotone tuples
Keywords: estimate for the variation distance of the compound Poisson approximation, compound Poisson distribution, Stein method. 
@article{PDMA_2014_7_a10,
     author = {A. A. Minakov},
     title = {Compound {Poisson} approximation for the distribution of the number of monotone tuples in random sequence},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {29--30},
     year = {2014},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2014_7_a10/}
}
TY  - JOUR
AU  - A. A. Minakov
TI  - Compound Poisson approximation for the distribution of the number of monotone tuples in random sequence
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2014
SP  - 29
EP  - 30
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/PDMA_2014_7_a10/
LA  - ru
ID  - PDMA_2014_7_a10
ER  - 
%0 Journal Article
%A A. A. Minakov
%T Compound Poisson approximation for the distribution of the number of monotone tuples in random sequence
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2014
%P 29-30
%N 7
%U http://geodesic.mathdoc.fr/item/PDMA_2014_7_a10/
%G ru
%F PDMA_2014_7_a10
A. A. Minakov. Compound Poisson approximation for the distribution of the number of monotone tuples in random sequence. Prikladnaya Diskretnaya Matematika. Supplement, no. 7 (2014), pp. 29-30. http://geodesic.mathdoc.fr/item/PDMA_2014_7_a10/

[1] Wolfowitz J., “Asymptotics distribution of runs up and down”, Ann. Math. Statist., 15 (1944), 163–172 | DOI | MR | Zbl

[2] David F. N., Barton D. E., Combinatorial Chance, Hafner Publishing Co., New York, 1962 | MR

[3] Pittel B. G., “Limiting behavior of a process of runs”, Ann. Probab., 9:1 (1981), 119–129 | DOI | MR | Zbl

[4] Chryssaphinou O., Papastavridis S., Vaggelatou E., “Poisson approximation for the non-overlapping appearances of several words in Markov chains”, Combinatorics, Probability and Computing, 10:4 (2001), 293–308 | DOI | MR | Zbl

[5] Mezhennaya N. M., “Mnogomernaya normalnaya teorema dlya chisla monotonnykh serii zadannoi dliny v ravnoveroyatnoi sluchainoi posledovatelnosti”, Obozrenie prikladnoi i promyshlennoi matematiki, 14:3 (2007), 503–505

[6] Roos V., “Stein's method for compound Poisson approximation: The local approach”, Ann. Appl. Probab., 4:4 (1994), 1177–1187 | DOI | MR | Zbl

[7] Barbour A. D., Chen L. H. Y., Loh W.-L., “Compound Poisson approximation for nonnegative random variables via Stein's method”, Ann. Appl. Probab., 20:4 (1992), 1843–1866 | DOI | MR | Zbl