A Central Limit Theorem Associated with the Transformed Two-Parameter Poisson–Dirichlet Distribution
Fang Xu · Journal of Applied Probability · 2009
In this paper we introduce the transformed two-parameter Poisson–Dirichlet distribution on the ordered infinite simplex. Furthermore, we prove the central limit theorem related to this distribution when both the mutation rateθand the selection rateσbecome 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 ofσandθ.