On approximation of the tails of the binomial distribution with these of the poisson law | Sciact - Система учета научной деятельности ИМ СО РАН

On approximation of the tails of the binomial distribution with these of the poisson law Научная публикация

Журнал

Mathematics
, E-ISSN: 2227-7390

Вых. Данные

Год: 2021, Том: 9, Номер: 8, Номер статьи : 845, Страниц : DOI: 10.3390/math9080845

Ключевые слова

Binomial distribution; Esscher transformation; Poisson approximation

Авторы

Nagaev S. ¹ , Chebotarev V. ²

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2	Computing Center, Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, 680000, Russian Federation

A subject of this study is the behavior of the tail of the binomial distribution in the case of the Poisson approximation. The deviation from unit of the ratio of the tail of the binomial distribution and that of the Poisson distribution, multiplied by the correction factor, is estimated. A new type of approximation is introduced when the parameter of the approximating Poisson law depends on the point at which the approximation is performed. Then the transition to the approximation by the Poisson law with the parameter equal to the mathematical expectation of the approximated binomial law is carried out. In both cases error estimates are obtained. A number of conjectures are made about the refinement of the known estimates for the Kolmogorov distance between binomial and Poisson distributions. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Nagaev S. , Chebotarev V.
On approximation of the tails of the binomial distribution with these of the poisson law
Mathematics. 2021. V.9. N8. 845 . DOI: 10.3390/math9080845 WOS Scopus OpenAlex

Web of science:	WOS:000644531300001
Scopus:	2-s2.0-85104112842
OpenAlex:	W3156381157

БД	Цитирований
Scopus	1
OpenAlex	1