摘要
在传统Beta模型基础上,采取与e指数n次多项式函数乘积方式,构造了一种参数可有限扩展的线性模型——Beta柔性扩展模型.据对全国数学建模分组数据的拟合实验,该模型的均方误差达到10^(-9)数量级水平.对19个国家收入分配分组数据进行多个模型的估计误差对比,证明该模型的拟合质量总体上优于对比模型.探索性提出的“固定参数+柔性参数”线性建模方式和“递次回归、择优筛选”的分组数据逼近机制,为提高洛伦兹曲线拟合精度提供了一种可参考的新方法、新选择.
Based on the traditional Beta model,a parameter was constructed by multiplying with e exponential polynomial function of n degree Beta Flexible Extension Model:A linear model with finite extension.The mean square error of the model reaches to the level of 10-9,according to the fitting experiment of the national mathematical modeling group data.By comparing the estimation errors of multiple models for the grouped data of income distribution in 19 countries,it is proved that the fitting quality of this model is generally better than that of the comparison model.In this paper,the linear modeling method of"fixed parameter+flexible parameter"and the grouping data approximation mechanism of"successive regression and selective screening"are put forward exploratively,which provide a new method and a new choice for improving the fitting accuracy of Lorentz curve.
作者
谭诗斌
TAN Shi-bin(Institute of Poverty Reduction and Development,Huazhong University of Science and Technology,Wuhan 430074,China)
出处
《数学的实践与认识》
2023年第7期154-168,共15页
Mathematics in Practice and Theory
