Total variation distance for poisson subset numbers - Goldstein, L; Reinert, G (2006)
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.