ABSTRACT
This chapter considers objective or non-informative Bayesian estimation of the population size, where the marginal model for the frequency count data is a member of the "Kemp" family of distributions. These were introduced by A. Kemp in 1968 and have since received attention in a variety of settings. Which are interested in them here because while the simplest Kemp distributions are the Poisson and gamma-mixed Poisson or negative binomial, the other members of the family are little known, un-"named," and most importantly not necessarily mixed Poisson. Thus they represent interesting candidates for marginal count distributions that depart from the classical mixed-Poisson scenario. Furthermore, they possess an appealing property in terms of the simplicity of their ratios of probabilities p(j + 1)/p(j), which was exploited in Willis and Bunge to produce a (frequentist) population-size estimation procedure based on nonlinear regression. The Kemp distributions are defined in terms of their probability generating functions.
