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.
Markov chains Stochastic vortices Parameter inference Open populations Delta method
This is a preview of subscription content, log in to check access.
Feller, W. 1966. An introduction to probability theory and its applications, 2nd ed. New York, John Wiley and Sons.zbMATHGoogle Scholar
Guerreiro, G., and J. Mexia. 2004. An alternative approach to bonus malus. Disc. Math. Probability Stat., 24(2), 197–213.MathSciNetzbMATHGoogle Scholar
Guerreiro, G., and J. Mexia. 2008. Stochastic vortices in periodically reclassified populations. Disc. Math. Probability Stat., 28(2), 209–227.MathSciNetCrossRefGoogle Scholar
Guerreiro, G., J. Mexia, and M. Miguens. 2010. A model for open populations subject to periodical re-classifications. J. Stat. Theory Pract., 4(2), 303–321.MathSciNetCrossRefGoogle Scholar
Schott, J. 1997. Matrix analysis for statistics. New York, Wiley Series in Probability and Statistics.zbMATHGoogle Scholar
Staff, P., and M. Vagholkar. 1971. Stationary distributions of open markov processes in discrete time with application to hospital planning. J. Appl. Probability, 8(4), 668–680.MathSciNetCrossRefGoogle Scholar
Tiago de Oliveira, J. 1982. The delta-method for obtention of asymptotic distributions; Applications. Publications Inst. Stat. Univ. Paris, 27, 49–70.zbMATHGoogle Scholar
Vassiliou, P. 1997. The evolution of the theory of non-homogeneous markov systems. Appl. Stochastic Models Data Anal., 13(3–4), 159–176.MathSciNetCrossRefGoogle Scholar