Total variation distance for poisson subset numbers

Journal article

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 Poisson distribution in this regime. © Birkhäuser Verlag, Basel 2006.

Authors: Goldstein, L; Reinert, G

• Publication status: Published
• Journal: ANNALS OF COMBINATORICS
• Volume: 10
• Issue: 3
• Pages: 333-341
• Publication date: 2006-12-01
• DOI: 10.1007/s00026-006-0291-9
• EISSN: 0219-3094
• ISSN: 0218-0006
• Language: English
• Keywords: surprisology; Stein's method; size biasing; Poisson approximation