Analysis of a Modified Gompertz Model Based on Nonlinear Least Squares Method

This paper proposes a modified Gompertz model with a constant free term based on the classical Gompertz model. Different from the three-sum method for determining the parameters of classical Gompertz model, this paper construct an optimization problem with the help of nonlinear least squares method. Moreover, employing the Levenberg-Marquardt method and the MATLAB software, the numerilal solution of the optimization problem is found. A numerilal example is provided in this paper. Finally, this paper uses this model to forecast the consumption level of Chinese rural residents, and the results illustrate the modified Gompertz model provides accurate prediction.