English

A Sub-Gaussian Berry-Esseen Theorem for the Hypergeometric Distribution

Probability 2007-06-13 v1 Statistics Theory Statistics Theory

Abstract

In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeometric distribution for weak convergence to a Normal limit. We establish a Berry-Esseen theorem for the Hypergeometric distribution solely under this necessary and sufficient condition. We further derive a nonuniform Berry-Esseen bound where the tails of the difference between the Hypergeometric and the Normal distribution functions are shown to decay at a sub-Gaussian rate.

Cite

@article{arxiv.math/0602276,
  title  = {A Sub-Gaussian Berry-Esseen Theorem for the Hypergeometric Distribution},
  author = {Soumendra N. Lahiri and A. Chatterjee and T. Maiti},
  journal= {arXiv preprint arXiv:math/0602276},
  year   = {2007}
}