基于Schur-凸的不完全信息下的不平等性比较  

Comparison of Inequality Under Incomplete Information and Based on Schur-Convex Function

作　　者：李棒 余旌胡[1] Li Bang;Yu Jinghu(Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 43007)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《数学物理学报（A辑）》2018年第2期334-349,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601400);中央高校基本科研业务费专项资金(2017IB012)~~

摘　　要：不平等问题渐渐成为全世界的热点话题,不平等指标也显得越来越重要.由于在不平等度量中,数据采集需要耗费大量成本,如何减少数据采集量就能比较不平等程度,这是一个有趣的问题,目前没有找到相关文献.由于不平等度量指标与Schur-凸函数有着直接关联,该文以Schur-凸函数为基础,通过给出在变量向量中少量已知分量值的情况下,确定其变量向量优超上界和优超下界的方法,给出判断变量向量间优超关系的充分条件.利用该条件即能比较不平等程度.以Shannon熵为例,给出了所得充分条件下,不平等度量上的应用.With the inequality increasingly prominent, the indicator to measure inequity is more and more important. Because of significant cost to collect data in inequality measure, it is very interesting to ask how to reduce the amount of data acquisition to compare the degree of inequality. The literatures on inequality keep silent on this problem. Since the indicator to measure inequity has a direct association with the Schur-convex function, based on the Schur-convex function and under the conditions of a few known variable values, this paper gives the sufficient conditions of the relationship of majorization between two variable vectors though determining the upper and lower bounds of majorization. Using this condition, we can compare the degree of inequality. And the application of Shannon entropy in inequality measure is given.

关 键 词：Shannon熵 Schur-凸函数 优超关系 不平等度量 充分条件 

分 类 号：O213[理学—概率论与数理统计]