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The Number of Collisions for the Occupancy Problem with Unequal Probabilities

Part of: Game theory Combinatorial probability

Published online by Cambridge University Press:  22 February 2016

Toshio Nakata
Toshio Nakata*
Affiliation:
Fukuoka University of Education
*
∗ Postal address: Department of Mathematics, Fukuoka University of Education, Akama-Bunkyomachi, Munakata, Fukuoka, 811-4192, Japan. Email address: nakata@fukuoka-edu.ac.jp
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Abstract

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In this article we study a number of collisions concerning a simple occupancy problem with unequal probabilities. Using combinatorial arguments and negative associations of random variables, we have several limit theorems, namely, a weak law of large numbers and a Poisson law of small numbers including the Chen-Stein estimate.

Keywords

Urn modelcollisionnegative associationPoisson approximation

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 91A60: Probabilistic games; gambling
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 168 - 185
Copyright
© Applied Probability Trust 

Footnotes

Dedicated to Professor Masafumi Yamashita on the occasion of his 60th birthday.

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