一类Lorentz曲线的本质属性与拟合研究

Properties of a Class of Lorentz Curve and fitting Research

给出曲线族L(p)=p~α(1-(1-p)~β)~γ,0<β<1是Lorentz曲线的充分必要条件为:α≥0,γ≥0且α+γ≥1.结果是已有相关结论的推广.在此基础上,在一类Lorentz曲线族中选择了一条最佳曲线作为衡量国家收入分配的指标.用2013全国研究生数学建模竞赛E题数据,得到了相当精确的结果(均方误差精确到10^(-6).

In this paper, we show that function L（p）=p^a（1-（1-p）^β）^γ,0〈β〈1 is Lorentz curve if and only if α≥0,γ≥0 and α＋γ≥1. In a family of function, we give a Lorentz curve to solve National Mathematical Modeling Contest for Postgraduates. Its optimization is showed such as mean squared error at10-6.