Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22064
Barbour, A D; Månsson, M (2000). Compound Poisson approximation and the clustering of random points. Advances in Applied Probability, 32(1):19-38.
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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, largely because the approximating distribution does not satisfy the simplifying condition that iλi be decreasing.
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||Compound Poisson approximation; Stein's method|
|Deposited On:||04 Mar 2010 11:03|
|Last Modified:||23 Nov 2012 14:18|
|Publisher:||Applied Probability Trust|
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