Precise Deviations for the Ewens-Pitman Model
Abstract
In this paper, we derive an integral representation for the distribution of the number of types Kn in the Ewens-Pitman model. Based on this representation, we also establish precise large deviations and precise moderate deviations for Kn. After careful examination, we find that the rate function exhibits a second-order phase transition and the critical point is α=12.
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