Parameter Estimation Of Bertalanffy Growth Curve Equation And Equations

Up to now,the mathematical model of population dynamics has been one of the most classical models that have been deeply studied and widely applied in the field of biological mathematics.The mathematical model of population dynamics often appears in the form of differential,which describes the law of the change of the research object with the continuous change of time.lt is necessary to estimate the parameter value and initial value of the model based on the actual observation data.This is of great significance for predicting the law of population development and providing theoretical guidance and decision-making basis for relevant departments.This is known as parameter estimation.Linear statistical model is widely used in modem statistics.It is the basic model for other statistical models and is widely used in biology,economy,business,finance,medicine and other fields.Therefore,how to apply the linear statistical model with complete theoretical system to the widely used nathematical model of population dynamics is the main purpose of this paper.Bertalanffy growth equation is one of the most important mathematical models of population dynamics.Firstly,Bertalanffy growth equation with differential form is transformed into several linear equations by finite difference method.At the same time,the continuous differential equation is transformed into discrete difference equation.That is,backward difference approaches differential quotient,bidirectional difference approaches differential quotient,and two direction weighted difference approaches differential quotient.Then the linear least squares estimation method is used to estimate the parameters of the discrete Bertalanffy growth equation.By the time an example is given to verify the applicability of Bertalanffy growth equation and the validity of parameter estimation.In addition,the theoretical knowledge of seemingly uncorrelated linear models in mathematical statistics is applied to several seemingly unrelated but actually related Bertalanffy growth equations,and the parameters of Bertalanffy growth equations are estimated by using the least square estimation method and two direction weighted difference least square estimation method.Finally,through experimental data to verify that the parameter estimation with system correlation is better than that with independent modeling.