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Distance between sampling with and without replacement

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  • A. J. Stam

Abstract

Summary Two random samples of size n are taken from a set containing N objects of H types, first with and then without replacement. Let d be the absolute (L1‐)distance and I the Kullback‐Leibler information distance between the distributions of the sample compositions without and with replacement. Sample composition is meant with respect to types; it does not matter whether order of sampling is included or not. A bound on I and d is derived, that depends only on n, N, H. The bound on I is not higher than 2I. For fixed H we have d0, I0 as N if and only if n/N0. Let Wr be the epoch at which for the r‐th time an object of type I appears. Bounds on the distances between the joint distributions of W1., Wr without and with replacement are given.

Suggested Citation

  • A. J. Stam, 1978. "Distance between sampling with and without replacement," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(2), pages 81-91, June.
    • Handle: RePEc:bla:stanee:v:32:y:1978:i:2:p:81-91
    DOI: 10.1111/j.1467-9574.1978.tb01387.x
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