Shifted Binomial Approximation for the Ewens Sampling Formula (Ii)

Abstract

The Ewens sampling formula is well-known as the distribution of a random partition of the positive integer n into components. For the number Kn of distinct components of the formula, Yamato (2017a) gives the approximations to the distribution of Kn by using the shifted Binomial distributions and recommends the approximations II and IV.1 among them. We examine these two approximations furthermore, and compare them with the shifted Poisson approximation (Yamato (2017b)) and the Normal approximation (Yamato et al. (2015)). As applications of the approximation II, we give the two examples.