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Total variation distance for poisson subset numbers

Abstract:

Let n be an integer and A 0,..., A k random subsets of {1,..., n} of fixed sizes a 0,..., a k , respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable W = |∩j=0kAj|, 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 aj → ∞ for all j = 0,..., k, showing that W has an asymptotic...

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Publication status:
Published

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Publisher copy:
10.1007/s00026-006-0291-9

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
Journal:
ANNALS OF COMBINATORICS More from this journal
Volume:
10
Issue:
3
Pages:
333-341
Publication date:
2006-12-01
DOI:
EISSN:
0219-3094
ISSN:
0218-0006
Language:
English
Keywords:
Pubs id:
pubs:97539
UUID:
uuid:f27da31f-aafb-440a-9ceb-29cef637b2d2
Local pid:
pubs:97539
Source identifiers:
97539
Deposit date:
2012-12-19

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