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The limit distribution of the number of rare mutants

Published online by Cambridge University Press:  14 July 2016

Mark Finkelstein ,
Howard G. Tucker  and
Jerry Alan Veeh
Mark Finkelstein*
Affiliation:
University of California, Irvine
Howard G. Tucker*
Affiliation:
University of California, Irvine
Jerry Alan Veeh*
Affiliation:
Auburn University
*
∗Postal address: Department of Mathematics, University of California, Irvine, CA 92717, USA.
∗Postal address: Department of Mathematics, University of California, Irvine, CA 92717, USA.
∗∗Postal address: Department of Algebra, Combinatorics, and Analysis, Auburn University, AL 36849, USA.
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Abstract

We study the number of mutants in a mutation process in which reverse mutation is allowed and in which both normal and mutant organisms reproduce at the same rate. Under a mild side condition on the rate of forward mutation we find necessary and sufficient conditions for the number of mutants to converge in distribution. We find the probability generating function of the limit distribution, when it exists. We present an example which shows that the mild side condition cannot be relaxed.

Keywords

MUTATION PROCESSESCONVERGENCE IN LAWINFINITELY DIVISIBLE DISTRIBUTION FUNCTIONSPOISSON DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 239 - 250
Copyright
Copyright © Applied Probability Trust 1990 

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References

Brown, T. C. (1984) Poisson approximation and the definition of the Poisson process. Amer. Math. Monthly 91, 116–123.Google Scholar
Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Finkelstein, M. and Tucker, H. G. (1989) A law of small numbers for a mutation process. Math. Biosci. 95, 85–98.CrossRefGoogle ScholarPubMed
Wang, Y. H. (1986) Coupling methods in approximations. Canad. J. Statist. 14, 69–74.Google Scholar