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, [alpha] and [theta], corresponding to the stable component and the gamma component respectively. The moderate deviation principle is established for the distribution when [theta] approaches infinity, and the large deviation principle is established when both [alpha] and [theta] approach zero.