::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online calculator computes the following Concentration statistics: entropy, maximum entropy, normalized entropy, exponential index, Lorenz curve, Herfindahl index, Gini coefficient, and concentration coefficient. To be used with (absolute) frequencies.

Enter (or paste) your data delimited by hard returns.

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Source code of R module

library(ineq) my_minimum <- min(x) if(my_minimum < 0) { stop("Negative values are not allowed.") } myLength <- length(x) myMaximumEntropy <- log(myLength) mySum <- sum(x) myProportion <- x/mySum myEntropy <- -sum(myProportion * log(myProportion)) myNormalizedEntropy <- myEntropy / myMaximumEntropy myDifference <- myMaximumEntropy - myEntropy myTheilEntropyIndex <- entropy(x,parameter=1,na.rm=T) myExponentialIndex <- exp(-myEntropy) myHerfindahlMeasure <- sum(myProportion^2) myHerfindahl <- conc(x,type="Herfindahl",na.rm=T) myRosenbluth <- conc(x,type="Rosenbluth",na.rm=T) myNormalizedHerfindahlMeasure <- (myHerfindahlMeasure - 1/myLength) / (1 - 1/myLength) myGini <- Gini(x,na.rm=T) myConcentrationCoefficient <- myLength/(myLength -1)*myGini myRS <- RS(x,na.rm=T) myAtkinson <- Atkinson(x,na.rm=T) myKolm <- Kolm(x,na.rm=T) myCoefficientOfVariation <- var.coeff(x,square=F,na.rm=T) mySquaredCoefficientOfVariation <- var.coeff(x,square=T,na.rm=T) bitmap(file="plot1.png") plot(Lc(x)) grid() dev.off() bitmap(file="plot2.png") plot(Lc(x),general=T) grid() dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Concentration - Ungrouped Data",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Measure",header=TRUE) a<-table.element(a,"Value",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of Categories",header=F) a<-table.element(a,myLength,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Maximum Entropy",header=F) a<-table.element(a,myMaximumEntropy,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Entropy",header=F) a<-table.element(a,myEntropy,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Normalised Entropy",header=F) a<-table.element(a,myNormalizedEntropy,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Max. Entropy - Entropy",header=F) a<-table.element(a,myDifference,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Theil Entropy Index",header=F) a<-table.element(a,myTheilEntropyIndex,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Exponential Index",header=F) a<-table.element(a,myExponentialIndex,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Herfindahl",header=F) a<-table.element(a,myHerfindahl,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Normalised Herfindahl",header=F) a<-table.element(a,myNormalizedHerfindahlMeasure,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Rosenbluth",header=F) a<-table.element(a,myRosenbluth,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Gini",header=F) a<-table.element(a,myGini,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Concentration",header=F) a<-table.element(a,myConcentrationCoefficient,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Ricci-Schutz (Pietra)",header=F) a<-table.element(a,myRS,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Atkinson",header=F) a<-table.element(a,myAtkinson,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Kolm",header=F) a<-table.element(a,myKolm,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Coefficient of Variation",header=F) a<-table.element(a,myCoefficientOfVariation,header=F) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Squared Coefficient of Variation",header=F) a<-table.element(a,mySquaredCoefficientOfVariation,header=F) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2021), Concentration and Inequality (v1.0.2) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_concentration.wasp/

The R code is based on :

F A Cowell: Measurement of Inequality, 2000, in A B Atkinson / F Bourguignon (Eds): Handbook of Income Distribution, Amsterdam

F A Cowell: Measuring Inequality, 1995 Prentice Hall/Harvester Wheatshef

Marshall / Olkin: Inequalities: Theory of Majorization and Its Applications, New York 1979 (Aca- demic Press)

M Hall / N Tidemann: Measures of Concentration, 1967, JASA 62, 162-168

B C Arnold: Majorization and the Lorenz Order: A Brief Introduction, 1987, Springer

To cite Wessa.net in publications use:
Wessa, P. (2025), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : wessa.net

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