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Asymptotic distribution for the coupon — collector's and sampling-tagging problems, when tagging affects catchability

Published online by Cambridge University Press:  14 July 2016

Ester Samuel-Cahn
Ester Samuel-Cahn*
Affiliation:
Hebrew University, Jerusalem
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Abstract

The coupon-collector's and sampling tagging problems are considered, under the model that each tagged element is γ > 0 times as likely to be caught at the next stage as every untagged element. Let WN (γ, k) and SN (γ, j) denote, respectively, the waiting time until k + 1 distinct elements are obtained, and the number of distinct elements in a sample of size j, when the population size is N. Complete characterisations are obtained for the limiting distributions of WN (γ, k) and SN (γ, j), in terms of the rates at which k and j tend to infinity with N.

Keywords

ASYMPTOTIC DISTRIBUTIONCOUPON-COLLECTINGSAMPLING-TAGGINGTAGGING AFFECTS CATCHABILITYWAITING TIME

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 625 - 628
Copyright
Copyright © Applied Probability Trust 1975 

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References

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