摘要
洛伦兹曲线是用来描述社会收入分配状况的一种曲线,能够精确有效地拟合洛伦兹曲线是进行收入分配定量分析的基础.基于洛伦兹曲线的经济学规律和数学特点,提出了一种新的指数函数多项式拟合洛伦兹曲线的线性模型,并讨论研究模型的矩阵广义逆和线性最小二乘求解方法.通过与5个典型的非线性拟合模型的实例对比分析,验证了方法具有收敛稳定、精度高、对噪声不敏感的优点.
Lorenz curve is used to describe social income distribution. It is the basis of quan- titative analysis of the income distribution that precisely and effectively fitting Lorenz curve. Based on the law of economics and mathematical characteristics of Lorenz curve, this paper proposes a new exponential polynomial fitting linear model of Lorenz curve, discussed and researched generalized inverse matrix and linear least square method of the model. Through comparative analysis with five typical instance of nonlinear fitting model, this method was verified with the advantages of convergence stability, high precision and insensitive to noise.
出处
《数学的实践与认识》
CSCD
北大核心
2014年第21期44-51,共8页
Mathematics in Practice and Theory
