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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_concentration.wasp
Title produced by softwareConcentration and Inequality
Date of computationMon, 18 Dec 2017 16:15:07 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/18/t1513610160zd5bsiexz74g2p8.htm/, Retrieved Mon, 13 May 2024 23:16:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310194, Retrieved Mon, 13 May 2024 23:16:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPaper
Estimated Impact71

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Concentration and Inequality] [Lorenz ] [2017-12-18 15:15:07] [2fb711e06e7eb81d34c9e51edb934d8a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
10.5
10
9.5
8.5
5
5.5
6.5
6
10.5
11
8.5
4
7
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9
9.5
10
8.5
9.5
9.5
10.5
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10.5
12
7.5
9.5
7.5
12
6
12
11
12.5
8
8.5
10
11.5
8
11
8.5
5.5
11.5
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8.5
9.5
13
10.5
9.5
9.5
9.5
11
8
8.5
6
9.5
5
9.5
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9
9
9.5
8
9.5
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12
10.5
10
8
9.5
10.5
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10
17
12
11
10.5
11
9.5
8.5
8.5
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12
13.5
11.5
11
9
5
8
10.5
10
10
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10
9
8.5
10
5
8.5
12.5
11
11.5
8
11
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14
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7
9.5
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10
10
10.5
7.5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310194&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310194&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Concentration - Ungrouped Data
MeasureValue
Number of Categories120
Maximum Entropy4.78749174278205
Entropy4.76324317436052
Normalised Entropy0.994935016136982
Max. Entropy - Entropy0.0242485684215232
Theil Entropy Index0.0242485684215236
Exponential Index0.00853787463136898
Herfindahl0.00872372850032795
Normalised Herfindahl0.000393675798650036
Rosenbluth0.00944340698182829
Gini0.117550122602048
Concentration0.118537938758368
Ricci-Schutz (Pietra)0.0799473532381365
Atkinson0.012461386483571
Kolm2.24777118420615
Coefficient of Variation0.21644264838371
Squared Coefficient of Variation0.0468474200393542

\begin{tabular}{lllllllll}
\hline
Concentration - Ungrouped Data \tabularnewline
Measure & Value \tabularnewline
Number of Categories & 120 \tabularnewline
Maximum Entropy & 4.78749174278205 \tabularnewline
Entropy & 4.76324317436052 \tabularnewline
Normalised Entropy & 0.994935016136982 \tabularnewline
Max. Entropy - Entropy & 0.0242485684215232 \tabularnewline
Theil Entropy Index & 0.0242485684215236 \tabularnewline
Exponential Index & 0.00853787463136898 \tabularnewline
Herfindahl & 0.00872372850032795 \tabularnewline
Normalised Herfindahl & 0.000393675798650036 \tabularnewline
Rosenbluth & 0.00944340698182829 \tabularnewline
Gini & 0.117550122602048 \tabularnewline
Concentration & 0.118537938758368 \tabularnewline
Ricci-Schutz (Pietra) & 0.0799473532381365 \tabularnewline
Atkinson & 0.012461386483571 \tabularnewline
Kolm & 2.24777118420615 \tabularnewline
Coefficient of Variation & 0.21644264838371 \tabularnewline
Squared Coefficient of Variation & 0.0468474200393542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310194&T=1

[TABLE]
[ROW][C]Concentration - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][/ROW]
[ROW][C]Number of Categories[/C][C]120[/C][/ROW]
[ROW][C]Maximum Entropy[/C][C]4.78749174278205[/C][/ROW]
[ROW][C]Entropy[/C][C]4.76324317436052[/C][/ROW]
[ROW][C]Normalised Entropy[/C][C]0.994935016136982[/C][/ROW]
[ROW][C]Max. Entropy - Entropy[/C][C]0.0242485684215232[/C][/ROW]
[ROW][C]Theil Entropy Index[/C][C]0.0242485684215236[/C][/ROW]
[ROW][C]Exponential Index[/C][C]0.00853787463136898[/C][/ROW]
[ROW][C]Herfindahl[/C][C]0.00872372850032795[/C][/ROW]
[ROW][C]Normalised Herfindahl[/C][C]0.000393675798650036[/C][/ROW]
[ROW][C]Rosenbluth[/C][C]0.00944340698182829[/C][/ROW]
[ROW][C]Gini[/C][C]0.117550122602048[/C][/ROW]
[ROW][C]Concentration[/C][C]0.118537938758368[/C][/ROW]
[ROW][C]Ricci-Schutz (Pietra)[/C][C]0.0799473532381365[/C][/ROW]
[ROW][C]Atkinson[/C][C]0.012461386483571[/C][/ROW]
[ROW][C]Kolm[/C][C]2.24777118420615[/C][/ROW]
[ROW][C]Coefficient of Variation[/C][C]0.21644264838371[/C][/ROW]
[ROW][C]Squared Coefficient of Variation[/C][C]0.0468474200393542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310194&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Concentration - Ungrouped Data
MeasureValue
Number of Categories120
Maximum Entropy4.78749174278205
Entropy4.76324317436052
Normalised Entropy0.994935016136982
Max. Entropy - Entropy0.0242485684215232
Theil Entropy Index0.0242485684215236
Exponential Index0.00853787463136898
Herfindahl0.00872372850032795
Normalised Herfindahl0.000393675798650036
Rosenbluth0.00944340698182829
Gini0.117550122602048
Concentration0.118537938758368
Ricci-Schutz (Pietra)0.0799473532381365
Atkinson0.012461386483571
Kolm2.24777118420615
Coefficient of Variation0.21644264838371
Squared Coefficient of Variation0.0468474200393542


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software 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')