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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 computationThu, 09 Dec 2021 15:21:34 +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/2021/Dec/09/t1639059917d9ooiq7tfdq6ypx.htm/, Retrieved Tue, 14 May 2024 03:53:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319574, Retrieved Tue, 14 May 2024 03:53:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48

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] [concentrazione] [2021-12-09 14:21:34] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35
40
28
33
16
21
50
25
44
52
28
60
58
36
18

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=319574&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=319574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319574&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 Categories15
Maximum Entropy2.70805020110221
Entropy2.63623094155035
Normalised Entropy0.973479347051017
Max. Entropy - Entropy0.0718192595518556
Theil Entropy Index0.0718192595518555
Exponential Index0.0716307418618141
Herfindahl0.0761245674740484
Normalised Herfindahl0.0101334651507662
Rosenbluth0.084946908182386
Gini0.215196078431372
Concentration0.230567226890756
Ricci-Schutz (Pietra)0.158823529411765
Atkinson0.0364618135860765
Kolm17.6915805526721
Coefficient of Variation0.376654366907815
Squared Coefficient of Variation0.141868512110727

\begin{tabular}{lllllllll}
\hline
Concentration - Ungrouped Data \tabularnewline
Measure & Value \tabularnewline
Number of Categories & 15 \tabularnewline
Maximum Entropy & 2.70805020110221 \tabularnewline
Entropy & 2.63623094155035 \tabularnewline
Normalised Entropy & 0.973479347051017 \tabularnewline
Max. Entropy - Entropy & 0.0718192595518556 \tabularnewline
Theil Entropy Index & 0.0718192595518555 \tabularnewline
Exponential Index & 0.0716307418618141 \tabularnewline
Herfindahl & 0.0761245674740484 \tabularnewline
Normalised Herfindahl & 0.0101334651507662 \tabularnewline
Rosenbluth & 0.084946908182386 \tabularnewline
Gini & 0.215196078431372 \tabularnewline
Concentration & 0.230567226890756 \tabularnewline
Ricci-Schutz (Pietra) & 0.158823529411765 \tabularnewline
Atkinson & 0.0364618135860765 \tabularnewline
Kolm & 17.6915805526721 \tabularnewline
Coefficient of Variation & 0.376654366907815 \tabularnewline
Squared Coefficient of Variation & 0.141868512110727 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319574&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]15[/C][/ROW]
[ROW][C]Maximum Entropy[/C][C]2.70805020110221[/C][/ROW]
[ROW][C]Entropy[/C][C]2.63623094155035[/C][/ROW]
[ROW][C]Normalised Entropy[/C][C]0.973479347051017[/C][/ROW]
[ROW][C]Max. Entropy - Entropy[/C][C]0.0718192595518556[/C][/ROW]
[ROW][C]Theil Entropy Index[/C][C]0.0718192595518555[/C][/ROW]
[ROW][C]Exponential Index[/C][C]0.0716307418618141[/C][/ROW]
[ROW][C]Herfindahl[/C][C]0.0761245674740484[/C][/ROW]
[ROW][C]Normalised Herfindahl[/C][C]0.0101334651507662[/C][/ROW]
[ROW][C]Rosenbluth[/C][C]0.084946908182386[/C][/ROW]
[ROW][C]Gini[/C][C]0.215196078431372[/C][/ROW]
[ROW][C]Concentration[/C][C]0.230567226890756[/C][/ROW]
[ROW][C]Ricci-Schutz (Pietra)[/C][C]0.158823529411765[/C][/ROW]
[ROW][C]Atkinson[/C][C]0.0364618135860765[/C][/ROW]
[ROW][C]Kolm[/C][C]17.6915805526721[/C][/ROW]
[ROW][C]Coefficient of Variation[/C][C]0.376654366907815[/C][/ROW]
[ROW][C]Squared Coefficient of Variation[/C][C]0.141868512110727[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319574&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 Categories15
Maximum Entropy2.70805020110221
Entropy2.63623094155035
Normalised Entropy0.973479347051017
Max. Entropy - Entropy0.0718192595518556
Theil Entropy Index0.0718192595518555
Exponential Index0.0716307418618141
Herfindahl0.0761245674740484
Normalised Herfindahl0.0101334651507662
Rosenbluth0.084946908182386
Gini0.215196078431372
Concentration0.230567226890756
Ricci-Schutz (Pietra)0.158823529411765
Atkinson0.0364618135860765
Kolm17.6915805526721
Coefficient of Variation0.376654366907815
Squared Coefficient of Variation0.141868512110727


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')