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Comparison of Sampling Schemes with and without Replacement

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Abstract

An urn contains colored balls, \(a\) ~balls of each of \(N\) different colors. The balls are drawn sequentially and equiprobably, one ball at a time, and then each drawn ball drawn is either returned to the urn (sampling with replacement) or left outside the urn (sampling without replacement). The drawing continues until some \(k\) colors are drawn at least \(m\) ~times each. Observable statistics are the numbers \(\mu _r\), \(r = 1,2, \ldots\), of colors that have appeared precisely \(r\) ~times each by the stopping time. The asymptotic behavior as \(N \to \infty\) of these values for each of the two sampling models is studied; the possibility of their use for identifying the model is discussed.

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Authors and Affiliations

  1. Moscow State Institute of Electronics and Mathematics, Russia

    G. I. Ivchenko

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  1. G. I. Ivchenko
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Ivchenko, G.I. Comparison of Sampling Schemes with and without Replacement. Mathematical Notes 73, 183–191 (2003). https://doi.org/10.1023/A:1022102924007

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  • DOI: https://doi.org/10.1023/A:1022102924007

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