Parameter estimation in multifactor uncertain population model

Abstract

This paper extends the traditional multifactor population model from a probabilistic background to an uncertain background, allowing us to better account for the fact that the birth and death rates are sometimes affected by different, independent uncertain noises. The theory of multifactor uncertain differential equation is applied to analyze the novel model. First, a multifactor uncertain population model is developed and the solution of the model is obtained. Secondly, the stability in measure and stability in distribution of the multifactor uncertain population model are studied respectively, and the relationship between the two kinds of stability is further discussed. Then, a method of moment estimation based on residuals is proposed for the unknown parameters in the multifactor uncertain population model. Finally, an example is given to illustrate the validity and rationality of the parameter estimation method.