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Ewens-Pitman model has been successfully applied to various fields includingBayesian statistics. There are four important estimators$K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n},M_{1,m}^{(n)}$ are related to discovery probability. Their asymptotic behavior,such as large deviation principle, has already been discussed in [4],[1] and[2]. Moderate deviation principle is also discussed in [3] with some speedrestriction. In this article, we will apply complex asymptotic analysis to showthat this speed restriction is unnecessary.

Some Moderate Deviations for Ewens-Pitman Sampling Model