## Article

#### Title: Moderate Deviations for Ewens-Pitman Sampling Models

##### Issue: Volume 80 Series A Part 2 Year 2018
###### Abstract
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the Poisson-Dirichlet distribution with parameter $\alpha$ \in [0, 1)$and$\theta > − $\alpha$. Given a sample of size $n$ from the population, two important statistics are the number $K_n$ of different types in the sample, and the number $M_{l, n}$ of different types with frequency $l$ in the sample. We establish moderate deviation principles for $(K_n)_{n \ge 1}$ and $(M_{l, n})_{n \ge 1}$. Corresponding rate functions are explicitly identified, which help in revealing a critical scale and in understanding the exact role of the parameters $\alpha$ and $\theta$.