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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 computationWed, 16 Feb 2022 23:15:48 +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/2022/Feb/16/t16450498433x4zdc5vj9gm8zg.htm/, Retrieved Wed, 22 May 2024 15:20:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319641, Retrieved Wed, 22 May 2024 15:20:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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] [] [2022-02-16 22:15:48] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19,0142
19,3591
18,1271
19,117
17,4516
19,9219
19,1823
18,1073
16,132
16,3489
15,3737
16,8836
19,4425
16,7027
15,5555
18,4142
16,119
16,1499
14,0406
17,3857
19,0302
23,2022
15,7916
17,3628
14,4647
17,7904
14,087
18,3571
15,0053
13,5792
15,9513
14,1961
14,7569
14,6411
15,5663
12,6109
12,8912
15,2774
14,9464
16,0203
14,3762
15,4509
15,5105
14,2117
16,5118
13,4452
14,3703
12,6933
14,638
21,4254
13,4509
13,5555
16,3285
14,8086
21,279
16,3805
15,4997
15,5883
15,1415
13,5313
12,5784
14,1387
12,5949
21,279
16,4421
22,0127
12,5813
0
13,032
16,5304
13,3991
22,8003
21,279
13,2589
21,4254
21,4254
15,9111
15,4818
13,135
12,0713
21,1069
14,6537
13,4088
13,4846
14,898
18,605
11,792
13,2176
15,406
18,581
14,142
13,6971
14,4587
12,5163
13,8396
17,7936
22,2304
11,4139
22,2574
15,2371
11,7328
18,581
13,356
11,6651
13,0219
14,4006
15,9796
25,8791
15,1965
13,5205
15,5245
14,2474
12,5819
13,3072
11,7095
14,0288
14,1011
13,1571
14,0367
13,1672
11,9818
13,5205
13,9726
13,4707
13,0249
13,3665
13,2552
14,8897
18,581
12,786
16,4457
13,7298
13,3245
29,7497
16,7371
14,3667
12,8917
12,1446
11,1726
13,712
13,8045
11,7371
15,8137
13,5313
15,1433
12,5443
14,2891
12,0129
15,8484
13,9389
13,2643
11,9157
14,5107
14,2909
18,7425
14,699
13,7975
15,3113
11,7013
13,4984
11,3435
11,638
22,0766
22,1418
13,908
16,1295
11,5769
11,4913
12,673
14,727
16,5976
16,8635
12,3499
14,9389
12,9998
22,1418
15,0847
13,27
13,9652
15,707
22,1987
15,2892
15,6484
13,9702
13,5977
15,9219
12,9451
14,9353
15,6629
13,2376
16,9984
21,9562
25,4723
16,8093
16,6241
21,1429
14,2748
15,8324
20,4061
18,2286
13,9672
15,3631
12,9055
16,4566
15,8765
17,8447
19,8724
14,2128
12,8624
16,2064
21,8178
25,4723
16,1634
13,1344
14,0921
17,1003
14,9895
13,7042
17,153
18,9282
17,6722
19,4932
16,6923
13,7842
18,7042
14,874
19,4582
18,5405
17,4832
20,9196
17,412
19,2811
18,7677
19,9852
24,4309
19,7337
18,4062
18,6397
18,1697
18,6135
20,2632
18,3774
23,5084
26,7899
22,9468
22,3903
23,0452
19,4397
21,2074
22,0338
19,185
24,0326
25,266
23,5327
20,2494
21,2122
20,4476
20,9151
21,0413
32,1813
17,8607
16,3009
16,3009
20,7805
18,4703
13,8922
13,4162
16,9474
13,8435
15,2513
12,5049
14,3594
18,5715
17,6014
16,5334
13,9953
11,5974
18,581
11,3471
14,8623
18,7632
12,8128
13,464
16,6465
13,227
24,1526
14,0285
12,5423
13,5564
13,0532
14,0069
12,2838
12,786
14,0235
14,8909
12,3693
18,581
14,6748
11,2541
17,8537
15,0697
12,2954
13,1221
15,8386
15,3185
12,2616
19,1513
13,6835
14,2917
15,3104
15,5382
11,6127
15,5355
13,0042
12,8521
22,7055
22,1365
13,9538
13,3178
14,5892
19,8833
17,9163
22,7283
21,2729
19,8808
20,5497
20,409
20,5497
24,7581
21,4355
21,1859
20,8246
25,192
24,7216

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319641&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319641&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Concentration - Ungrouped Data
MeasureValue
Number of Categories334
Maximum Entropy5.8111409929767
EntropyNaN
Normalised EntropyNaN
Max. Entropy - EntropyNaN
Theil Entropy Index0.0232635275467877
Exponential IndexNaN
Herfindahl0.00315013846226461
Normalised Herfindahl0.000156595334523666
Rosenbluth0.00341600128800154
Gini0.123533124368496
Concentration0.123904094711945
Ricci-Schutz (Pietra)0.090845194448955
Atkinson0.0143431777567322
Kolm10.5374337885874
Coefficient of Variation0.22835552631014
Squared Coefficient of Variation0.052146246396381

\begin{tabular}{lllllllll}
\hline
Concentration - Ungrouped Data \tabularnewline
Measure & Value \tabularnewline
Number of Categories & 334 \tabularnewline
Maximum Entropy & 5.8111409929767 \tabularnewline
Entropy & NaN \tabularnewline
Normalised Entropy & NaN \tabularnewline
Max. Entropy - Entropy & NaN \tabularnewline
Theil Entropy Index & 0.0232635275467877 \tabularnewline
Exponential Index & NaN \tabularnewline
Herfindahl & 0.00315013846226461 \tabularnewline
Normalised Herfindahl & 0.000156595334523666 \tabularnewline
Rosenbluth & 0.00341600128800154 \tabularnewline
Gini & 0.123533124368496 \tabularnewline
Concentration & 0.123904094711945 \tabularnewline
Ricci-Schutz (Pietra) & 0.090845194448955 \tabularnewline
Atkinson & 0.0143431777567322 \tabularnewline
Kolm & 10.5374337885874 \tabularnewline
Coefficient of Variation & 0.22835552631014 \tabularnewline
Squared Coefficient of Variation & 0.052146246396381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319641&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]334[/C][/ROW]
[ROW][C]Maximum Entropy[/C][C]5.8111409929767[/C][/ROW]
[ROW][C]Entropy[/C][C]NaN[/C][/ROW]
[ROW][C]Normalised Entropy[/C][C]NaN[/C][/ROW]
[ROW][C]Max. Entropy - Entropy[/C][C]NaN[/C][/ROW]
[ROW][C]Theil Entropy Index[/C][C]0.0232635275467877[/C][/ROW]
[ROW][C]Exponential Index[/C][C]NaN[/C][/ROW]
[ROW][C]Herfindahl[/C][C]0.00315013846226461[/C][/ROW]
[ROW][C]Normalised Herfindahl[/C][C]0.000156595334523666[/C][/ROW]
[ROW][C]Rosenbluth[/C][C]0.00341600128800154[/C][/ROW]
[ROW][C]Gini[/C][C]0.123533124368496[/C][/ROW]
[ROW][C]Concentration[/C][C]0.123904094711945[/C][/ROW]
[ROW][C]Ricci-Schutz (Pietra)[/C][C]0.090845194448955[/C][/ROW]
[ROW][C]Atkinson[/C][C]0.0143431777567322[/C][/ROW]
[ROW][C]Kolm[/C][C]10.5374337885874[/C][/ROW]
[ROW][C]Coefficient of Variation[/C][C]0.22835552631014[/C][/ROW]
[ROW][C]Squared Coefficient of Variation[/C][C]0.052146246396381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319641&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 Categories334
Maximum Entropy5.8111409929767
EntropyNaN
Normalised EntropyNaN
Max. Entropy - EntropyNaN
Theil Entropy Index0.0232635275467877
Exponential IndexNaN
Herfindahl0.00315013846226461
Normalised Herfindahl0.000156595334523666
Rosenbluth0.00341600128800154
Gini0.123533124368496
Concentration0.123904094711945
Ricci-Schutz (Pietra)0.090845194448955
Atkinson0.0143431777567322
Kolm10.5374337885874
Coefficient of Variation0.22835552631014
Squared Coefficient of Variation0.052146246396381


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')