Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-22171
Barbour, A D; Utev, S (1998). Solving the Stein equation in compound Poisson approximation. Advances in Applied Probability, 30(2):449-475.
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The accuracy of compound Poisson approximation can be estimated using Stein's method in terms of quantities similar to those which must be calculated for Poisson approximation. However, the solutions of the relevant Stein equation may, in general, grow exponentially fast with the mean number of `clumps', leading to many applications in which the bounds are of little use. In this paper, we introduce a method for circumventing this difficulty. We establish good bounds for those solutions of the Stein equation which are needed to measure the accuracy of approximation with respect to Kolmogorov distance, but only in a restricted range of the argument. The restriction on the range is then compensated by a truncation argument. Examples are given to show that the method clearly outperforms its competitors, as soon as the mean number of clumps is even moderately large.
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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:||Stein's method; compound Poisson; distributional approximation|
|Deposited On:||07 Apr 2010 13:55|
|Last Modified:||05 Apr 2016 13:26|
|Publisher:||Applied Probability Trust|
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