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Sampling Without Replacement: Approximation to the Probability Distribution

Part of: Limit theorems Distribution theory

Published online by Cambridge University Press:  09 April 2009

J. N. Darroch ,
M. Jirina  and
T. P. Speed
J. N. Darroch
Affiliation:
Department of MathematicsThe Flinders University of South Australia Bedford Park, S. A. 5042, Australia
M. Jirina
Affiliation:
Division of Mathematics and Statistics C.S.I.R.O. Yarralumla Canberra, A.C.T. 2600, Australia
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Abstract

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Let P be the probability distribution of a sample without replacement of size n from a finite population represented by the set N={1,2,…N}. For each r=0, 1, …, an approximation Pr is described such that the uniform norm ‖P − Pr‖ is of order (n2/N)r+1 if n2/N→0. The approximation Pr is a linear combination of uniform probability product-measures concentrated on certain subspaces of the sample space Nn.

MSC classification

Secondary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 197 - 213
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Aigner, M., Combinational Theory (Springer-Verlag, 1979).CrossRefGoogle Scholar
[2]Comtet, L., Advanced Combinatorix (Reidel, 1974).CrossRefGoogle Scholar
[3]Freedman, D., ‘A remark on the difference between sampling with or without replacement’, J. Amer. Stat. Assoc. 72 (1977), 681.CrossRefGoogle Scholar