On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law
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...
| Published in: | Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-04-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/8/845 |
| _version_ | 1850331970156888064 |
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| author | Sergei Nagaev Vladimir Chebotarev |
| author_facet | Sergei Nagaev Vladimir Chebotarev |
| author_sort | Sergei Nagaev |
| collection | DOAJ |
| container_title | Mathematics |
| description | 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. |
| format | Article |
| id | doaj-art-ac7e05ab3bc84e239cf75f91240bfa77 |
| institution | Directory of Open Access Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-ac7e05ab3bc84e239cf75f91240bfa772025-08-19T23:17:44ZengMDPI AGMathematics2227-73902021-04-019884510.3390/math9080845On Approximation of the Tails of the Binomial Distribution with These of the Poisson LawSergei Nagaev0Vladimir Chebotarev1Sobolev Institute of Mathematics, 630090 Novosibirsk, RussiaComputing Center, Far Eastern Branch of the Russian Academy of Sciences, 680000 Khabarovsk, RussiaA 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.https://www.mdpi.com/2227-7390/9/8/845binomial distributionpoisson approximationesscher transformation |
| spellingShingle | Sergei Nagaev Vladimir Chebotarev On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law binomial distribution poisson approximation esscher transformation |
| title | On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law |
| title_full | On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law |
| title_fullStr | On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law |
| title_full_unstemmed | On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law |
| title_short | On Approximation of the Tails of the Binomial Distribution with These of the Poisson Law |
| title_sort | on approximation of the tails of the binomial distribution with these of the poisson law |
| topic | binomial distribution poisson approximation esscher transformation |
| url | https://www.mdpi.com/2227-7390/9/8/845 |
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