Asymptotic results for the two-parameter Poisson–Dirichlet distribution

The two-parameter Poisson–Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and gamma subordinators with the two parameters, αα and θθ, corresponding to the stable component and the gamma component respectively. The moderate deviation principle is established for the distribution when θθ approaches infinity, and the large deviation principle is established when both αα and θθ approach zero.