无量纲化方法的有效性评价  

Validity Evaluation of Dimensionless Methods

作　　者：李兴奇[1] 高晓红[2] Li Xingqi;Gao Xiaohong(School of Management and Economics,Chuxiong Normal University,Chuxiong Yunnan 675000,China;School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong Yunnan 675000,China)

机构地区：[1]楚雄师范学院管理与经济学院,云南楚雄675000 [2]楚雄师范学院数学与计算机科学学院,云南楚雄675000

出　　处：《统计与决策》2021年第15期24-28,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11261001);云南省应用基础研究计划青年项目(2017FD152);楚雄师范学院校级一般项目(XJYB2007)。

摘　　要：无量纲化的原则是最大限度地消除各指标间的差异,同时尽可能保留指标的内部信息,构建一套不依赖综合评价结果的评价标准来判别无量纲化方法的优劣,将会使评价结果更具实时性和独立性。文章根据分布不变性、变异特征不变性和效率最优性原则构建无量纲化方法的有效性评价标准,通过理论研究和数值模拟实验比较了不同无量纲化方法的有效性。结果表明:线性无量纲化方法不会改变数据的分布特征,伸缩法不会改变数据的分布特征和变异特征,均值化和归一化是现有无量纲化方法中效率较高的;当数据的分布类型发生变化时,无量纲化方法的有效性也会随之改变,在无量纲化方法选择前需要充分考虑数据的分布类型。The principle of dimensionless methods is to eliminate the differences between indicators to the maximum extent,while preserving the internal information of indicators as much as possible.To establish a set of evaluation criteria independent of the comprehensive evaluation results to judge the advantages and disadvantages of the dimensionless method will make the evaluation results more real-time and independent.According to the principles of distribution invariance,variation characteristic invariance and efficiency optimality,this paper constructs the validity evaluation standard of dimensionless methods,and then compares the validity of different dimensionless methods by theoretical researches and numerical simulation experiments.The results are shown as follows:The linear dimensionless methods do not change the distribution characteristics of data;the scaling methods do not change the distribution characteristics and variation characteristics of data;averaging and normalization are the most efficient dimensionless methods.When the distribution type of data changes,the validity of the dimensionless methods will also change,so the distribution type of data should be fully considered before the selection of the dimensionless method.

关 键 词：无量纲化 有效性 评价标准 数值模拟 

分 类 号：C812[社会学—统计学] O213.9[理学—概率论与数理统计]