统计与决策2024，Vol.40Issue(24)：42-47,6.DOI:10.13546/j.cnki.tjyjc.2024.24.007
无量纲化方法的效用测度及最优无量纲化模型构建
Utility Measure of Dimensionless Method and Construction of Optimal Dimensionless Model
摘要
Abstract
In order to solve the problem of difficulty in choosing the dimensionless method in the process of data processing,this paper first statistically measures the utility of dimensionless methods,using distribution characteristics change,variation char-acteristics change,differential information loss and information loss rate,respectively,to measure the negative utility of dimension-less methods,the scatter-degree approach and differentiation degree to measure the positive utility of dimensionless methods,and statistical test to judge the effectiveness of dimensionless methods.Secondly,with dimensionless effectiveness as the constraint condition and the minimum negative utility or the maximum positive utility as the objective function,the paper constructs the opti-mal dimensionless models with the minimal distribution characteristics loss,the minimal variation characteristics loss,the minimal differential information loss,the minimal information loss rate,the highest grade pulled open,the highest differentiation degree,re-spectively.Finally,the paper uses numerical simulation experiments to solve the optimal model.The results are shown as below:Small adjustment of translational scale or telescopic scale may have a huge impact on its effect.Therefore,great care must be paid in application,and the choice of method should not be based solely on personal experience.Through the optimal dimensionless model,the dimensionless difference between indexes can be eliminated,and the useful information in indexes can be protected from loss to the greatest extent,so as to improve the scientificity of data processing.The statistical test of the utility of the dimen-sionless method can accurately judge whether the dimensional difference between indicators has been eliminated at a given confi-dence level,and prevent excessive data processing.关键词
无量纲化/效用测度/变异系数/拉开档次Key words
dimensionless/utility measure/coefficient of variation/scatter-degree分类
社会科学引用本文复制引用
高晓红,李兴奇..无量纲化方法的效用测度及最优无量纲化模型构建[J].统计与决策,2024,40(24):42-47,6.基金项目
国家自然科学基金资助项目(12461075) （12461075）
云南省地方本科高校基础研究联合专项面上项目(202301BA070001-054 （）
202301BA070001-059) （）
