Barbour, A D; Holst, L (1989). Some applications of the Stein-Chen method for proving Poisson convergence. Advances in Applied Probability, 21(1):74-90.
Let W be a sum of Bernoulli random variables and Uλ a Poisson random variable having the same mean λ =EW. Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance between W and Uλ are given. These bounds are applied to problems of occupancy, using sampling with and without replacement and Pólya sampling, of capture-recapture, of spacings and of matching and ménage.
Let W be a sum of Bernoulli random variables and Uλ a Poisson random variable having the same mean λ =EW. Using the Stein-Chen method and suitable couplings, general upper bounds for the variational distance between W and Uλ are given. These bounds are applied to problems of occupancy, using sampling with and without replacement and Pólya sampling, of capture-recapture, of spacings and of matching and ménage.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Language: | English |
| Date: | 1989 |
| Deposited On: | 13 Apr 2010 12:32 |
| Last Modified: | 23 Jan 2022 14:49 |
| Publisher: | Applied Probability Trust |
| ISSN: | 0001-8678 |
| OA Status: | Closed |
| Free access at: | Related URL. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.2307/1427198 |
| Official URL: | http://www.jstor.org/stable/1427198 |
| Related URLs: | http://user.math.uzh.ch/barbour/pub/Barbour/BHolst.pdf (Author) |
Barbour, A D