Sensitivity Characteristics And Application Of Multidimensional Bonferroni Index And Multidimensional De Vergottini Index

There are development gaps between countries in the world,and income gaps between individuals within each country.Therefore,resource allocation has always been a common and concerned issue.Since the new century,the problem of polarization in the distribution of social resources has become increasingly serious.The general quantitative measurement methods of the polarization of resource allocation include the Gini index and the Lorentz curve.On this basis,some scholars have proposed the Bonferroni index(abbreviated as "B index")and De Vergottini index(abbreviated as "V index").Among them,the one-dimensional B index is considered to be sensitive to groups with low and medium resource ownership,and the one-dimensional V index is considered to be sensitive to groups with high resource ownership.In addition,the imbalance between individuals and between countries is manifested in many aspects in reality.For example,there are imbalances in education,medical care,and income between countries.If a one-dimensional inequality index is used to correct For its measurement,it is necessary to reduce the dimensionality of the data,but the dimensionality reduction will lose part of the information carried by the data,and the one-dimensional inequality index cannot reflect reality well.Therefore,the original one-dimensional inequality index needs to be modified to adapt it to multi-dimensional data.This article is developed in this context.First of all,this article introduces the Lorentz curve,Gini index,one-dimensional B index and V index,expands the B index and V index to multiple dimensions through the multidimensional expansion framework,and obtains the empirical algorithm of the multidimensional B index and V index,so that it has calculation On the feasibility.Then verify whether the multidimensional B index and V index conform to the general axioms of inequality index,and obtain reasonable intervals of B index and V index through data simulation,and verify the sensitivity characteristics of the multidimensional B index and V index.Finally,based on the aforementioned Vergottini Index theory and CHFS data,empirical research on the imbalance of household assets in my country,and draw certain conclusions and recommendations.