## The sampling formula and Laplace transform associated with the two-parameter Poisson-Dirichlet distribution.(English)Zbl 1251.60010

Pitman’s sampling formula is used to derive the Laplace transform of the two-parameter Poisson-Dirichlet distribution, and it is shown that the sampling formula uniquely determines the Laplace transform. In particular this implies that both the Laplace transform and the sampling formula characterize the two-parameter Poisson-Dirichlet distribution.
The author then derives the Laplace transform for the infinitely-many-neutral-alleles model, which is applied to prove a central limit theorem as the mutation rate converges to infinity.
Finally the Laplace transform of a non neutral model undergoing selection is derived.

### MSC:

 60C05 Combinatorial probability 60F05 Central limit and other weak theorems
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### References:

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