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 θ > 0 and for all sufficiently large n ∈ N, the unique maximum of the Ewens ...

Ewens (1972) proposed a model in the infinite allele framework for populations with neutrality of all alleles at a particular locus. This paper proposes a generalisation of Ewens' result for situations where there is a form of weak selection. The models considered here are continuous time, discrete state space Markov processes.

The ideas from Probabilistic Number Theory are useful in the study of measures on partitions of integers. Connection between the Ewens sampling formula in population genetics and the partitions of an integer generated by random permutations will be discussed. Functional limit theory for partial sum processes induced by Ewens sampling formula is reviewed. The results on limit processes with depe...

Fisher's logarithmic series model (Fisher et al. (1943)) is a classical model in statistical ecology. In this paper we show that this model is a key model linking three models discussed in Takemura (1997), i.e., Poisson-gamma model (Bethlehem et al. (1990)), Dirichlet-multinomial model (Takemura (1997)), and Ewens model (Ewens (1990)). This connection opens up the possibility of applying existi...

Fisher’s logarithmic series model (Fisher et al. (1943)) is a classical model in statistical ecology. In this paper we show that this model is a key model linking three models discussed in Takemura (1997), i.e., Poisson-gamma model (Bethlehem et al. (1990)), Dirichlet-multinomial model (Takemura (1997)), and Ewens model (Ewens (1990)). This connection opens up the possibility of applying existi...

Fisher's logarithmic series model (Fisher et al. (1943)) is a classical model in statistical ecology. In this paper we show that this model is a key model linking three models discussed in Takemura (1997), i.e., Poisson-gamma model (Bethlehem et al. (1990)), Dirichlet-multinomial model (Takemura (1997)), and Ewens model (Ewens (1990)). This connection opens up the possibility of applying existi...

The number of the unique individuals in the population is of great importance in evaluating the disclosure risk of a microdata set. We approach this problem by considering some basic superpopulation models including the gamma-Poisson model of Bethlehem et al. (1990). We introduce Dirichlet-multinomial model which is closely related but more basic than the gamma-Poisson model, in the sense that ...

We give a criterion for functionals of partitions to converge to a universal limit under a class of measures that “behaves like” the Ewens measure. Various limit theorems for the Ewens measure, most notably the Poisson-Dirichlet limit for the longest parts, the functional central limit theorem for the number of parts, and the Erdős-Turán limit for the product of parts, extend to these asymptoti...