Geodesic
Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays
Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 82-98 
A. M. Shoitov. Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays. Diskretnaya Matematika, Tome 14 (2002) no. 1, pp. 82-98. http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/
@article{DM_2002_14_1_a6,
     author = {A. M. Shoitov},
     title = {Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays},
     journal = {Diskretnaya Matematika},
     pages = {82--98},
     year = {2002},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/}
}
TY  - JOUR
AU  - A. M. Shoitov
TI  - Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays
JO  - Diskretnaya Matematika
PY  - 2002
SP  - 82
EP  - 98
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/
LA  - ru
ID  - DM_2002_14_1_a6
ER  - 
%0 Journal Article
%A A. M. Shoitov
%T Limit distributions of the number of sets of $H$-equivalent segments in an equiprobable polynomial scheme of arrays
%J Diskretnaya Matematika
%D 2002
%P 82-98
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/DM_2002_14_1_a6/
%G ru
%F DM_2002_14_1_a6

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

In this paper we study random variables which characterise collections of segments in an equiprobable polynomial scheme related by the $H$-equivalence. We give an upper bound for the variation distance between the distribution of the random variable $\xi_k(H)$ equal to the number of collections of $H$-equivalent segments and the Poisson distribution. We present sufficient conditions for the convergence of the distribution functions of the number of $H$-equivalent segments in the triangular array scheme of equiprobable polynomial trials to the normal law, the Poisson law, and the compound Poisson law.

[1] Buravlev S. M., “Povtoreniya s tochnostyu do perestanovki v posledovatelnosti nezavisimykh ispytanii”, Diskretnaya matematika, 11:1 (1999), 53–75 | MR | Zbl

[2] Buravlev S. M., “Povtoreniya s tochnostyu do perestanovok, obrazuyuschikh latinskii pryamougolnik”, Diskretnaya matematika, 12:1 (2000), 24–46 | MR | Zbl

[3] Zubkov A. M., Mikhailov V. G., “Predelnye raspredeleniya sluchainykh velichin, svyazannye s dlinnymi povtoreniyami v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatnostei i ee primeneniya, 19:1 (1974), 173–181 | DOI | MR | Zbl

[4] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1976 | MR | Zbl

[5] Medvedev Yu. I., Ivchenko G. I., “Asimptoticheskoe predstavlenie konechnykh raznostei ot stepennoi funktsii v proizvolnoi tochke”, Teoriya veroyatnostei i ee primeneniya, 10:1 (1965), 45–61

[6] Mikhailov V. G., “Predelnye raspredeleniya sluchainykh velichin, svyazannykh s mnogokratnymi dlinnymi povtoreniyami v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatnostei i ee primeneniya, 19, no. 1, 1974, 182–187

[7] Mikhailov V. G., “Predelnaya teorema Puassona dlya chisla $H$-sovpadenii tsepochek”, Obozrenie prikladnoi i promyshlennoi matematiki, 7:1 (2000), 123–124

[8] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, Moskva, 1982 | MR | Zbl

[9] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, Moskva, 1984

[10] Barbour A. D., Holst L., Janson S., Poisson approximation, Oxford Univ. Press, Oxford, 1992 | MR | Zbl

[11] Roos M., “Stein method for compound Poisson approximation: the local approach”, Ann. Appl. Probab., 4 (1994), 1177–1187 | DOI | MR | Zbl