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.

DOI:
https://doi.org/10.1090/S0002-9939-07-08676-5

Published electronically:
January 5, 2007

MathSciNet review:
2276664

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-07-08676-5

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.