J Austral Math Soc Ser A 44 pp197--213, 1988.

Sampling Without Replacement: Approximation to the Probability Distribution

J. N. Darroch, M. Jirina and T. P. Speed

Abstract

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 P_r is described such that the uniform norm ||P - P_r|| is of order (n²/N)^r+1 if n²/N ® 0. The approxiamtion P_r is a linear combination of uniform probability product-measures concentrated on certain subspaces of the sample space Nⁿ.

1980 AMS Subject Classification: 60F05, 62E20

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Authors

J. N. Darroch

Department of Mathematics, The Flinders University of South Australia, Beford Park, S. A. 5042, Australia.

M. Jirina

Department of Mathematics, The Flinders University of South Australia, Beford Park, S. A. 5042, Australia.

T. P. Speed

Division of Mathematics and Statistics, C.S.I.R.O., Yarralumla, Canberra, A.C.T. 2600, Australia.