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On the asymptotic behaviour of the extinction time of the simple branching process

Published online by Cambridge University Press:  01 July 2016

Anthony G. Pakes
Anthony G. Pakes*
Affiliation:
The University of Western Australia
*
∗Postal address: Department of Mathematics, The University of Western Australia, Nedlands, WA 6009, Australia.
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Abstract

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The time to extinction of a subcritical Galton–Watson branching process and the time of last mutation of its infinite-alleles version are maxima of independent random variables having an upper tail of geometric type, and hence they are not attracted to any extreme value distribution. It is shown that Anderson's asymptotic results for maxima of discrete variates are applicable, and this rectifies a false assertion made in respect to the infinite-alleles simple branching process.

Keywords

MAXIMAEXTREME VALUE DISTRIBUTION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 470 - 472
Copyright
Copyright © Applied Probability Trust 1989 

References

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