Stable Distributions for Open Populations subject to periodical re-classifications

Using a Markov model, we study the evolution of open populations subject to periodical reclassifications considering a random number of entrances. In this paper, we focus on the estimation of the subpopulations' relative sizes, obtaining maximum likelihood (ML) estimators, asymptotic distributions, and confidence regions. We show, under general conditions, that the stable distribution is dependent on the rate of entrances to the population. We illustrate the model by estimating the evolution of a population of a pension fund beneficiaries.