A group-dynamic model and the lost-games distribution

Abstract

The paper deals with the distribution of the size of naturally-occuring groups of individuals, where group size is determined by a birth-and-death process. A realistic new state-dependent time-homogeneous equilibrium process is put forward in which the birth rate and the death rate both approach upper asymptotes as group size increases. The outcome is a lost-games distribution. This is fitted to data on size of playgroups, using maximum-likelihood estimation, and provides a very satisfactory fit.

Keywords:

• state-dependent process
• time-homogeneous process
• maximum-likelihood
• inverse binomial distribution