Total Variation Distance for Poisson Subset Numbers |
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Authors: | Larry Goldstein Gesine Reinert |
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Affiliation: | (1) Department of Mathematics, University of Southern California, 3620 Vermont Avenue, Los Angeles, CA 90089-2532, USA;(2) Department of Statistics, University of Oxford, 1 South Parks Road, Oxford, OX1 3TG, UK |
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Abstract: | Let n be an integer and A0,..., Ak random subsets of {1,..., n} of fixed sizes a0,..., ak, respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable , the size of the intersection of the random sets, to a Poisson random variable Z with intensity λ = EW. In particular, the bound tends to zero when λ converges and for all j = 0,..., k, showing that W has an asymptotic Poisson distribution in this regime. Received February 24, 2005 |
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Keywords: | 60C05 62E17 |
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