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

Soumendra N. Lahiri·A. Chatterjee·T. Maiti
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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.

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BibTeXRIS

Soumendra N. Lahiri, A. Chatterjee, T. Maiti. 2006-02-13. A Sub-Gaussian Berry-Esseen Theorem for the Hypergeometric Distribution. https://arxiv.org/abs/math/0602276

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