On approximation of the tails of the binomial distribution with these of the poisson law Full article
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Mathematics
, E-ISSN: 2227-7390 |
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| Output data | Year: 2021, Volume: 9, Number: 8, Article number : 845, Pages count : DOI: 10.3390/math9080845 | ||||
| Tags | Binomial distribution; Esscher transformation; Poisson approximation | ||||
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Abstract:
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.
Cite:
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
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
Identifiers:
| Web of science: | WOS:000644531300001 |
| Scopus: | 2-s2.0-85104112842 |
| OpenAlex: | W3156381157 |