Distance between sampling with and without replacement |
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Authors: | A J Stam |
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Institution: | *Mathematisch Instituut, Rijksuniversiteit Groningen. |
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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 K ullback -L eibler 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 2 I. For fixed H we have d 0, I 0 as N if and only if n/N 0. Let W r 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 W 1., W r without and with replacement are given. |
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