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The collector's problem with group drawings

Published online by Cambridge University Press:  01 July 2016

Wolfgang Stadje
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗ Postal address: Fachbereich Mathematik/Informatik, Universität Osnabrück, Albrechtstrasse 28, 4500 Osnabrück, W. Germany.
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Abstract

We consider sampling with replacement of equiprobable groups of a fixed size m from a finite population S. Given a subset A ⊂ S, the distributions of (a) the number of distinct elements of A in a sample of size k and (b) the sample size necessary to obtain at least say n elements of A are given. Neat formulas are given especially for the expected values of these, as well as of some related random variables. Further we derive an optimal strategy to collect all elements of S under the assumptions that sampling one group costs α monetary units and that it is possible to purchase the elements which are missing at the end of the sampling procedure at a price of β > α/m per element.

Keywords

SAMPLING WITH REPLACEMENTOPTIMAL COLLECTING STRATEGY

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 866 - 882
Copyright
Copyright © Applied Probability Trust 1990 

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