指数函数与幂函数回归计算的极大似然法及其应用  

The Maximum Likelihood Method of Regression Calculate for Exponential Function and Power Function and Its Application

作　　者：张子贤[1] 刘玉伟 刘家春[1] ZHANG Zi-xian;LIU Yu-wei;LIU Jia-chun(School of Construction Equipment and Municipal Engineering,Jiangsu Vocational Institute of Architectural Technology,Xuzhou 221116,China;Bereau of Hydrologic and Water Resources Survey of Hebei Province Tangqin,Tangshan 063001,China)

机构地区：[1]江苏建筑职业技术学院建筑设备与市政工程学院,江苏徐州221116 [2]河北省唐山水文水资源勘测局,河北唐山063001

出　　处：《数学的实践与认识》2018年第24期217-222,共6页Mathematics in Practice and Theory

基　　金：住房与城乡建设部项目(2015-K7-009)

摘　　要：为提高拟合精度,研究了指数函数与幂函数非线性回归计算的极大似然法.分析表明,在指数函数与幂函数回归计算的因变量为正态随机变量的情况下,极大似然估计与非线性回归的最小二乘估计具有相同的结果;导出了极大似然法求解指数函数与幂函数回归参数的方程式,并给出了计算方法.此方法拟合因变量的残差平方和为最小.实例表明,本文方法拟合精度与高斯-牛顿法相当、显著优于线性化的回归方法,而计算方法要比高斯-牛顿法简单方便,易于实现.In order to heighten fitting accuracy,the maximum likelihood method of non-linear regression calculate for exponential function and power function were studied in this paper. The analysis indicates that the maximum likelihood estimate and nonlinear regression least square estimation have the same results when the dependent variable of regression calculate for exponential function and power function being normal random variable.The equations were deduced by maximum likelihood method to solve the regression parameters of exponential function and power function,and the calculation method was given.Residual sum of squares fitted the dependent variable is minimum by the method.Example shows that fitting accuracy of this paper method is as good as Gauss-Newton method and is notably better than the regression method of linearization,but calculation is simpler and easier to achieve than Gauss- Newton method.

关 键 词：指数函数 幂函数 线性化回归方法 非线性回归方法 极大似然法 残差平方和 拟合精度 

分 类 号：O212.1[理学—概率论与数理统计]