Studies Of Some Topics On Parameter Estimation In Gompertz Growth Curve Equation

Ecological mathematical models have rich theoretical contents and extensive practical background, at the same time, parameter estimation becomes one of the primary issues when a ecological mathematical model was created. The research and development about linear model system have long history, also produced many outstanding achievements.How to build a bridge between the linear models and ecological mathematical models with differential forms, apply the rich theory and methods summarized from linear models to ecological mathematical models, and provide an effective way for soving practical problems, are the main work of this paper.In this paper, the methods and principles of linear statistical models were used to estimate the parameters which given by the growth curve equations, meanwhile some appropriate adjustments were done for the selection of initial values to improve the fitting accuracy.On the basis of multivariate statistical analytical principles and methods, Gompertz growth curve models was constructed, then the two direction difference estimate method and two direction difference generalized weighted least squares estimate method were used to estimate the parameters of Gompertz growth curve models, moreover, the initial value was modified by choose average method, thereby improving the fitting accuracy and reducing fitting error of Gompertz growth curve models.In practical applications, because of some known or unknown factors, the correlation was often existed within the system more or less. However, the SUR model has the advantage of taking into account relevant information among equations. For this reason, the SUR model was considered to be applied in parameter estimation about Gompertz growth curve equations with correlation among each other. Thus, interrelated modeling platform for Gompert growth curve models with correlativity is built, and the parameter estimation has principles and basis of statistical estimation. At last, examples of practical applications verified that this method can optimize the model fitting.