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Sequential urn schemes and birth processes

Published online by Cambridge University Press:  01 July 2016

Lars Holst  and
Jürg Hüsler
Lars Holst*
Affiliation:
Uppsala University
Jürg Hüsler*
Affiliation:
University of Bern
*
∗Dept of Mathematics, Uppsala University, Thunbergsvägen 3, S-752 38 Uppsala, Sweden.
∗∗Dept of Mathematical Statistics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
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Abstract

An urn contains balls of different colours, which are randomly drawn one at a time. After each draw the number of balls in the urn with the same colour as the ball last drawn is changed. Special cases are sampling with and without replacement, and Pólya sampling. The drawing stops when a given number of colours has been drawn a given number of times. The number of times the different colours have been drawn is studied in this paper by imbedding the urn scheme in birth processes. Both exact and asymptotic results are obtained. In particular, waiting times for sampling with and without replacement and for Pólya sampling are considered.

Keywords

SAMPLING WITH AND WITHOUT REPLACEMENTPOLYA’S URN MODELSEQUENTIAL OCCUPANCYEXACT DISTRIBUTION THEORYASYMPTOTIC DISTRIBUTION THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 2 , June 1985 , pp. 257 - 279
Copyright
Copyright © Applied Probability Trust 1985 

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