Herding and clustering: Ewens vs. Simon–Yule models

Clustering has often described by Ewens Sampling Formula (ESF). Focusing the attention on the evergreen problem of the size of firms, we discuss the compatibility of empirical data and ESF. In order to obtain a power law for all sizes in the present paper we shall explore the route inspired by Yule, Zipf and Simon. It differs from the Ewens model both for destruction and creation. In particular the probability of herding is independent on the size of the herd. Computer simulations seem to confirm that actually the mean number of clusters of size i (the equilibrium distribution) follows the corresponding Yule distribution. Finally we introduce a finite Markov chain, that resembles the marginal dynamics of a cluster, which drives the cluster to a censored Yule distribution.