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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Berry-Esseen theorem for hypergeometric probabilities under minimal conditions


Authors: S. N. Lahiri and A. Chatterjee
Journal: Proc. Amer. Math. Soc. 135 (2007), 1535-1545
MSC (2000): Primary 60F05; Secondary 60G10, 62E20, 62D05.
Published electronically: January 5, 2007
MathSciNet review: 2276664
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Abstract: In this paper, we consider simple random sampling without replacement from a dichotomous finite population and derive a necessary and sufficient condition on the finite population parameters for a valid large sample Normal approximation to Hypergeometric probabilities. We then obtain lower and upper bounds on the difference between the Normal and the Hypergeometric distributions solely under this necessary and sufficient condition.


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Additional Information

S. N. Lahiri
Affiliation: Department of Statistics, Iowa State University, Ames, Iowa 50011
Address at time of publication: Department of Statistics, Texas A&M University, College Station, Texas 77843
Email: snlahiri@iastate.edu

A. Chatterjee
Affiliation: Department of Statistics, Iowa State University, Ames, Iowa 50011
Address at time of publication: Department of Statistics, Texas A&M University, College Station, Texas 77843
Email: cha@iastate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08676-5
PII: S 0002-9939(07)08676-5
Received by editor(s): April 12, 2005
Received by editor(s) in revised form: February 16, 2006
Published electronically: January 5, 2007
Additional Notes: This research was partially supported by NSF grant no. DMS 0306574.
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.