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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationMon, 15 Dec 2014 17:31:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/15/t1418664768ps84fz2w2akrz22.htm/, Retrieved Thu, 16 May 2024 20:50:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268784, Retrieved Thu, 16 May 2024 20:50:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [Gaussian] [2014-12-15 17:31:05] [21b927ddce509724d48ffb8407994bd0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.46923
1.36606
-3.47534
-2.89913
-1.50654
3.10755
3.85515
-0.203616
-3.46634
-0.0391273
-4.87992
-1.1216
0.223303
1.73095
-0.233539
-0.943214
0.811105
2.33878
-3.26949
0.940631
-3.45327
2.84757
-0.0457278
0.417186
-0.914617
-0.0715039
-0.985563
1.39428
0.528043
1.60632
-0.619856
1.94834
-0.705898
4.17762
-1.3081
1.16799
0.130515
0.251352
3.01642
0.253442
4.64622
-2.18698
1.22491
-1.01084
-2.57124
2.3186
-1.20771
1.97383
0.687828
2.40665
0.966223
-1.38651
0.472197
0.594499
-4.21268
-0.658803
2.44915
-4.30362
-1.78751
-1.16309
-0.816663
-1.11169
1.23777
-5.66383
0.882031
2.47499
1.97269
-0.350329
1.12672
-3.36727
1.79265
-1.89556
2.08237
1.44278
4.77541
-3.12845
-0.825404
0.888394
-2.38884
1.89966
0.94697
1.27055
-2.31261
1.15258
1.13686
0.323957
-0.225496
3.15018
-1.71691
1.17662
0.34972
-0.419565
2.75944
0.88401
2.36335
-0.0652071
1.52223
0.405327
0.252914
-1.20664
1.2719
-6.51597
1.82979
2.06149
-1.31551
1.86552
0.188742
1.97971
0.722507
-2.57618
-2.50956
2.39116
0.65538
0.369605
7.57766
1.72243
-0.890809
1.30362
1.91501
-0.636854
-3.28346
0.729232
2.57022
-1.21928
-1.0189
-1.02462
2.87673
-0.821116
1.99139
-0.574713
-3.68046
-1.71111
-1.61412
2.24133
0.153434
-2.40619
0.324171
2.55687
-1.85084
-1.98684
0.151709
-2.05271
1.89106
-2.05041
3.40154
0.120697
0.335348
-2.51077
-0.113755
1.58292
1.23692
-1.56225
1.35914
-1.14639
-0.73058
-0.461708
1.31137
-1.253
0.832946
3.27027
2.24115
0.0822816
0.361412
-2.53325
-1.33686
-0.993349
-0.407429
1.60689
1.76695
-1.15916
-1.25279
1.30106
-4.8393
-0.866651
2.76216
1.99686
2.45674
2.50745
1.77442
3.73404
2.95679
3.35175
2.45574
-0.136375
-2.66607
-1.94931
-6.04772
0.310603
-1.87887
0.214021
-0.43586
-1.19532
-2.48515
1.08102
1.64821
-2.35619
-1.03264
0.540648
0.341065
1.00231
-0.416175
-2.47881
-1.58639
-0.0547641
0.51898
-2.50553
0.347006
-4.06064
-6.18502
-1.68431
-5.99097
-0.853553
-1.63502
-4.01286
1.17264
1.2375
0.620227
-0.338094
1.58508
2.35076
-0.694053
0.812352
-0.801981
1.02658
0.906787
1.07402
-0.201061
0.621424
-2.43537

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268784&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268784&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth0.603098786176011
#Observations229

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.603098786176011 \tabularnewline
#Observations & 229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268784&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.603098786176011[/C][/ROW]
[ROW][C]#Observations[/C][C]229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268784&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:

Properties of Density Trace
Bandwidth0.603098786176011
#Observations229






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.7908091298980850.188399274826021
Epanechnikov0.8254710138844960.188486258516059
Rectangular0.9641185498301410.190685966625802
Triangular0.9294566658437290.187004922987444
Biweight0.8254710138844960.187743933055137
Cosine0.8601328978709070.18773424372874
Optcosine0.8254710138844960.188186693320723

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.790809129898085 & 0.188399274826021 \tabularnewline
Epanechnikov & 0.825471013884496 & 0.188486258516059 \tabularnewline
Rectangular & 0.964118549830141 & 0.190685966625802 \tabularnewline
Triangular & 0.929456665843729 & 0.187004922987444 \tabularnewline
Biweight & 0.825471013884496 & 0.187743933055137 \tabularnewline
Cosine & 0.860132897870907 & 0.18773424372874 \tabularnewline
Optcosine & 0.825471013884496 & 0.188186693320723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268784&T=2

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]0.790809129898085[/C][C]0.188399274826021[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.825471013884496[/C][C]0.188486258516059[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.964118549830141[/C][C]0.190685966625802[/C][/ROW]
[ROW][C]Triangular[/C][C]0.929456665843729[/C][C]0.187004922987444[/C][/ROW]
[ROW][C]Biweight[/C][C]0.825471013884496[/C][C]0.187743933055137[/C][/ROW]
[ROW][C]Cosine[/C][C]0.860132897870907[/C][C]0.18773424372874[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.825471013884496[/C][C]0.188186693320723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268784&T=2

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


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

Maximum Density Values
Kernelx-valuemax. density
Gaussian0.7908091298980850.188399274826021
Epanechnikov0.8254710138844960.188486258516059
Rectangular0.9641185498301410.190685966625802
Triangular0.9294566658437290.187004922987444
Biweight0.8254710138844960.187743933055137
Cosine0.8601328978709070.18773424372874
Optcosine0.8254710138844960.188186693320723


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = 0 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
if (par1 == '0') bw <- 'nrd0'
if (par1 != '0') bw <- as.numeric(par1)
par3 <- as.numeric(par3)
mydensity <- array(NA, dim=c(par3,8))
bitmap(file='density1.png')
mydensity1<-density(x,bw=bw,kernel='gaussian',na.rm=TRUE)
mydensity[,8] = signif(mydensity1$x,3)
mydensity[,1] = signif(mydensity1$y,3)
plot(mydensity1,main='Gaussian Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
mydensity1
bitmap(file='density2.png')
mydensity2<-density(x,bw=bw,kernel='epanechnikov',na.rm=TRUE)
mydensity[,2] = signif(mydensity2$y,3)
plot(mydensity2,main='Epanechnikov Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density3.png')
mydensity3<-density(x,bw=bw,kernel='rectangular',na.rm=TRUE)
mydensity[,3] = signif(mydensity3$y,3)
plot(mydensity3,main='Rectangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density4.png')
mydensity4<-density(x,bw=bw,kernel='triangular',na.rm=TRUE)
mydensity[,4] = signif(mydensity4$y,3)
plot(mydensity4,main='Triangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density5.png')
mydensity5<-density(x,bw=bw,kernel='biweight',na.rm=TRUE)
mydensity[,5] = signif(mydensity5$y,3)
plot(mydensity5,main='Biweight Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density6.png')
mydensity6<-density(x,bw=bw,kernel='cosine',na.rm=TRUE)
mydensity[,6] = signif(mydensity6$y,3)
plot(mydensity6,main='Cosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density7.png')
mydensity7<-density(x,bw=bw,kernel='optcosine',na.rm=TRUE)
mydensity[,7] = signif(mydensity7$y,3)
plot(mydensity7,main='Optcosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Properties of Density Trace',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bandwidth',header=TRUE)
a<-table.element(a,mydensity1$bw)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Observations',header=TRUE)
a<-table.element(a,mydensity1$n)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Density Values',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kernel',1,TRUE)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'max. density',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
a<-table.element(a,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
a<-table.element(a,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
a<-table.element(a,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
a<-table.element(a,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
a<-table.element(a,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
a<-table.element(a,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.element(a,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
a<-table.element(a,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
if (par2=='yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values',8,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.row.end(a)
for(i in 1:par3) {
a<-table.row.start(a)
a<-table.element(a,mydensity[i,8],1,TRUE)
for(j in 1:7) {
a<-table.element(a,mydensity[i,j],1)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}