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Weak limit for the stationary distribution of the infinite-alleles model

Published online by Cambridge University Press:  14 July 2016

Haim Avni
Haim Avni*
Affiliation:
The Weizmann Institute of Science
*
∗ Currently at the Israel Institute for Biological Research, P.O.B. 19, Nes-Ziona, Israel.
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Abstract

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models.

In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.

Keywords

ALLELE FREQUENCESGENERALIZED LAPLACE TRANSFORMORDER STATISTICSSAMPLE DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 459 - 472
Copyright
Copyright © Applied Probability Trust 1979 

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References

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