A central limit theorem associated with the transformed two-parameter Poisson--Dirichlet distribution
Fang Xu
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 392-401.
Abstract
In this paper we introduce the transformed two-parameter
Poisson--Dirichlet distribution ∏θ, ασ on
the ordered infinite simplex. Furthermore, we prove the central
limit theorem related to this distribution when both the mutation rate
θ and the selection rate
σ become large in a specified manner. As a consequence, we find
that the properly
scaled homozygosities have asymptotical normal behavior. In
particular, there is a certain phase transition with the limit
depending on the relative strength of σ and θ.
Primary Subjects: 60F05
Secondary Subjects: 92D10
Keywords: Poisson--Dirichlet distribution; two-parameter Poisson--Dirichlet distribution; homozygosity; GEM representation; selection
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676095
Digital Object Identifier: doi:10.1239/jap/1245676095
Zentralblatt MATH identifier:
05578814
Mathematical Reviews number (MathSciNet):
MR2535821
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