A Note on Estimating the Size of an Open Population of Stationary Size

A common model used to estimate the size of an animal population is to suppose that the population is closed and the size of the population is constant. Models for open populations allow the size of the population to vary. But stable populations are open and of a constant mean size. Here we examine inference under the assumption that the size of an open population has a stationary Poisson distribution. The situation in mind is where the number of animals an area can support has a stationary distribution, but the actual animals may change from occasion to occasion due to competition. We develop an estimator for a simple model that allows permanent emigration and immigration.