  Ewens-Pitman model has been successfully applied to various fields including
Bayesian 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 speed
restriction. In this article, we will apply complex asymptotic analysis to show
that this speed restriction is unnecessary.
