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Some applications of the Stein-Chen method for proving Poisson convergence


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.

Abstract

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.

Abstract

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.

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Additional indexing

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:05 Apr 2016 13:29
Publisher:Applied Probability Trust
ISSN:0001-8678
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)

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