scholarly journals Gaussian Limits Associated with the Poisson-Dirichlet Distribution and the Ewens Sampling Formula

2002 ◽  
Vol 12 (1) ◽  
pp. 101-124 ◽  
Author(s):  
Paul Joyce ◽  
Stephen M. Krone ◽  
Thomas G. Kurtz
Keyword(s):  
Dirichlet Distribution ◽  
Ewens Sampling Formula ◽  
Sampling Formula

Size-biased filtering of Poisson–Dirichlet samples with an application to partition structures in genetics

1986 ◽  
Vol 23 (4) ◽  
pp. 1008-1012 ◽  
Author(s):  
Fred M. Hoppe
Keyword(s):  
Characteristic Property ◽  
Dirichlet Distribution ◽  
Biased Sampling ◽  
Sampling Formula

A characteristic property of the Ewen sampling formula is shown to follow from the invariance under size-biased sampling of the Poisson–Dirichlet distribution.

The infinitely-many-neutral-alleles diffusion model by ages

1990 ◽  
Vol 22 (01) ◽  
pp. 1-24 ◽  
Author(s):  
S. N. Ethier
Keyword(s):  
Diffusion Model ◽  
Probability Distributions ◽  
Ewens Sampling Formula ◽  
Sample Paths ◽  
Sampling Formula ◽  
Frequent Allele

We discuss two formulations of the infinitely-many-neutral-alleles diffusion model that can be used to study the ages of alleles. The first one, which was introduced elsewhere, assumes values in the set of probability distributions on the set of alleles, and the ages of the alleles can be inferred from its sample paths. We illustrate this approach by proving a result of Watterson and Guess regarding the probability that the most frequent allele is oldest. The second diffusion model, which is new, assumes values in the set of probability distributions on the set of pairs (x, a), where x is an allele and a is its age. We illustrate this second approach by proving an extension of the Ewens sampling formula to age-ordered samples due to Donnelly and Tavaré.

A stability property of the Ewens sampling formula

1983 ◽  
Vol 20 (03) ◽  
pp. 449-459
Author(s):  
Stanley Sawyer
Keyword(s):  
Population Size ◽  
Error Bound ◽  
Mutation Rate ◽  
Stability Property ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Deleterious Alleles

An error bound for convergence to the Ewens sampling formula is given where the population size or mutation rate may vary from generation to generation, or the population is not yet at equilibrium. An application is given to a model of Hartl and Campbell about selectively-equivalent subtypes within a class of deleterious alleles, and a theorem is proven showing that the size of the deleterious class stays within bounds sufficient to apply the first result. Generalizations are discussed.

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