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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_concentration.wasp
Title produced by softwareConcentration and Inequality
Date of computationFri, 19 Oct 2018 04:10:20 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Oct/19/t15399151471160eyp6n0mq4n3.htm/, Retrieved Sun, 05 May 2024 09:29:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=315585, Retrieved Sun, 05 May 2024 09:29:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87

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] [] [2018-10-19 02:10:20] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13634
13717
18128
22943
23143
23422
27490
30918
34336
47970
48079
48448

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315585&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=315585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315585&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 time2 seconds
R ServerBig Analytics Cloud Computing Center






Concentration - Ungrouped Data
MeasureValue
Number of Categories12
Maximum Entropy2.484906649788
Entropy2.39777139826864
Normalised Entropy0.964934195203351
Max. Entropy - Entropy0.0871352515193613
Theil Entropy Index0.0871352515193612
Exponential Index0.0909203529274998
Herfindahl0.0980436265231118
Normalised Herfindahl0.0160475925706674
Rosenbluth0.108669682766519
Gini0.233150118673132
Concentration0.254345584007053
Ricci-Schutz (Pietra)0.178831135893039
Atkinson0.043680829667918
KolmInf
Coefficient of Variation0.42014701983632
Squared Coefficient of Variation0.176523518277341

\begin{tabular}{lllllllll}
\hline
Concentration - Ungrouped Data \tabularnewline
Measure & Value \tabularnewline
Number of Categories & 12 \tabularnewline
Maximum Entropy & 2.484906649788 \tabularnewline
Entropy & 2.39777139826864 \tabularnewline
Normalised Entropy & 0.964934195203351 \tabularnewline
Max. Entropy - Entropy & 0.0871352515193613 \tabularnewline
Theil Entropy Index & 0.0871352515193612 \tabularnewline
Exponential Index & 0.0909203529274998 \tabularnewline
Herfindahl & 0.0980436265231118 \tabularnewline
Normalised Herfindahl & 0.0160475925706674 \tabularnewline
Rosenbluth & 0.108669682766519 \tabularnewline
Gini & 0.233150118673132 \tabularnewline
Concentration & 0.254345584007053 \tabularnewline
Ricci-Schutz (Pietra) & 0.178831135893039 \tabularnewline
Atkinson & 0.043680829667918 \tabularnewline
Kolm & Inf \tabularnewline
Coefficient of Variation & 0.42014701983632 \tabularnewline
Squared Coefficient of Variation & 0.176523518277341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=315585&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]12[/C][/ROW]
[ROW][C]Maximum Entropy[/C][C]2.484906649788[/C][/ROW]
[ROW][C]Entropy[/C][C]2.39777139826864[/C][/ROW]
[ROW][C]Normalised Entropy[/C][C]0.964934195203351[/C][/ROW]
[ROW][C]Max. Entropy - Entropy[/C][C]0.0871352515193613[/C][/ROW]
[ROW][C]Theil Entropy Index[/C][C]0.0871352515193612[/C][/ROW]
[ROW][C]Exponential Index[/C][C]0.0909203529274998[/C][/ROW]
[ROW][C]Herfindahl[/C][C]0.0980436265231118[/C][/ROW]
[ROW][C]Normalised Herfindahl[/C][C]0.0160475925706674[/C][/ROW]
[ROW][C]Rosenbluth[/C][C]0.108669682766519[/C][/ROW]
[ROW][C]Gini[/C][C]0.233150118673132[/C][/ROW]
[ROW][C]Concentration[/C][C]0.254345584007053[/C][/ROW]
[ROW][C]Ricci-Schutz (Pietra)[/C][C]0.178831135893039[/C][/ROW]
[ROW][C]Atkinson[/C][C]0.043680829667918[/C][/ROW]
[ROW][C]Kolm[/C][C]Inf[/C][/ROW]
[ROW][C]Coefficient of Variation[/C][C]0.42014701983632[/C][/ROW]
[ROW][C]Squared Coefficient of Variation[/C][C]0.176523518277341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=315585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=315585&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 Categories12
Maximum Entropy2.484906649788
Entropy2.39777139826864
Normalised Entropy0.964934195203351
Max. Entropy - Entropy0.0871352515193613
Theil Entropy Index0.0871352515193612
Exponential Index0.0909203529274998
Herfindahl0.0980436265231118
Normalised Herfindahl0.0160475925706674
Rosenbluth0.108669682766519
Gini0.233150118673132
Concentration0.254345584007053
Ricci-Schutz (Pietra)0.178831135893039
Atkinson0.043680829667918
KolmInf
Coefficient of Variation0.42014701983632
Squared Coefficient of Variation0.176523518277341


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')