Mode and Edgeworth expansion for the Ewens distribution and the Stirling numbers
J. Integer Seq. 19(8), Article 16.8.8, 5 p. (2016)
Summary
Summary: We provide asymptotic expansions for the Stirling numbers of the first kind and, more generally, the Ewens (or Karamata-Stirling) distribution. Based on these expansions, we obtain some new results on the asymptotic properties of the mode and the maximum of the Stirling numbers and the Ewens distribution. For arbitrary $\theta0$ and for all sufficiently large $n\in\mathbb{N} $, the unique maximum of the Ewens probability mass function