Total Variation Distance for Poisson Subset Numbers |
| |
| Authors: | Larry Goldstein Gesine Reinert |
| |
| Institution: | (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 |
| |
| 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 |
| |
| Keywords: | 60C05 62E17 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
