Publication: Compound Poisson approximation and the clustering of random points
Compound Poisson approximation and the clustering of random points
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Barbour, A. D., & Månsson, M. (2000). Compound Poisson approximation and the clustering of random points. Advances in Applied Probability, 32(1), 19–38. https://doi.org/10.1239/aap/1013540020
Abstract
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Let n random points be uniformly and independently distributed in the unit square, and count the number W of subsets of k of the points which are covered by some translate of a small square C. If n|C| is small, the number of such clusters is approximately Poisson distributed, but the quality of the approximation is poor. In this paper, we show that the distribution of W can be much more closely approximated by an appropriate compound Poisson distribution CP(λ1, λ2,...). The argument is based on Stein's method, and is far from routine,
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- Barbour, Andrew D
- Månsson, Marianne
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Barbour, A. D., & Månsson, M. (2000). Compound Poisson approximation and the clustering of random points. Advances in Applied Probability, 32(1), 19–38. https://doi.org/10.1239/aap/1013540020
