A Sub-Gaussian Berry-Esseen Theorem For the Hypergeometric Distribution
نویسندگان
چکیده
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. AMS(2000) Subject Classification Primary 60F05; Secondary 60G10, 62E20, 62D05. Research partially supported by NSF grant no. DMS 0306574.
منابع مشابه
ar X iv : m at h / 06 02 27 6 v 1 [ m at h . PR ] 1 3 Fe b 20 06 A Sub - Gaussian Berry - Esseen Theorem For the Hypergeometric Distribution
In this paper, we derive a necessary and sufficient condition on the parameters of the Hypergeomet-ric 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 Hypergeo-metric and...
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