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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 26 Sep 2013 11:42:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Sep/26/t1380210195h3g03oewygsfzug.htm/, Retrieved Mon, 29 Apr 2024 15:48:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212153, Retrieved Mon, 29 Apr 2024 15:48:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2013-09-25 08:57:40] [c19d7b9cd6c492e87112b55d15521e82]
- RMPD    [Kernel Density Estimation] [] [2013-09-26 15:42:29] [5a3c7f9bb7dd641f8bd846ae07c7d6c7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19,4
19,4
19,4
19,5
19,5
19,5
28,7
28,7
28,7
21,8
21,8
21,8
20
20
20
22,6
22,6
22,6
22,4
22,4
22,4
18,6
18,6
18,6
16,2
16,2
16,2
13,8
13,8
13,8
24,1
24,1
24,1
19,9
19,9
19,9
22,3
22,3
22,3
20,9
20,9
20,9
23,5
23,5
23,5
23,1
23,1
23,1
25,7
25,7
25,7
19,7
19,7
19,7
23,1
23,1
23,1
20,7
20,7
20,7
18
18
18
16,9
16,9
16,9
24,4
24,4
24,4
15,5
15,5
15,5
18,4
18,4
18,4
16,2
16,2
16,2
20,6
20,6
20,6
19,8
19,8
19,8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&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 time7 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Properties of Density Trace
Bandwidth1.15594809522011
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.15594809522011 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.15594809522011[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&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
Bandwidth1.15594809522011
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.18590306681610.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.9894269807163 & 0.123346001589881 \tabularnewline
Epanechnikov & 20.2885460022413 & 0.118312241723669 \tabularnewline
Rectangular & 21.1859030668161 & 0.133784029034183 \tabularnewline
Triangular & 19.946695691927 & 0.121705072777611 \tabularnewline
Biweight & 20.245814713452 & 0.11898469760827 \tabularnewline
Cosine & 20.2030834246627 & 0.119538631114576 \tabularnewline
Optcosine & 20.245814713452 & 0.118582491716083 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&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]19.9894269807163[/C][C]0.123346001589881[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20.2885460022413[/C][C]0.118312241723669[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.1859030668161[/C][C]0.133784029034183[/C][/ROW]
[ROW][C]Triangular[/C][C]19.946695691927[/C][C]0.121705072777611[/C][/ROW]
[ROW][C]Biweight[/C][C]20.245814713452[/C][C]0.11898469760827[/C][/ROW]
[ROW][C]Cosine[/C][C]20.2030834246627[/C][C]0.119538631114576[/C][/ROW]
[ROW][C]Optcosine[/C][C]20.245814713452[/C][C]0.118582491716083[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&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
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.18590306681610.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.22863435560540.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.9894269807163 & 0.123346001589881 \tabularnewline
Epanechnikov & 20.2885460022413 & 0.118312241723669 \tabularnewline
Rectangular & 21.2286343556054 & 0.133784029034183 \tabularnewline
Triangular & 19.946695691927 & 0.121705072777611 \tabularnewline
Biweight & 20.245814713452 & 0.11898469760827 \tabularnewline
Cosine & 20.2030834246627 & 0.119538631114576 \tabularnewline
Optcosine & 20.245814713452 & 0.118582491716083 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&T=3

[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]19.9894269807163[/C][C]0.123346001589881[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20.2885460022413[/C][C]0.118312241723669[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.2286343556054[/C][C]0.133784029034183[/C][/ROW]
[ROW][C]Triangular[/C][C]19.946695691927[/C][C]0.121705072777611[/C][/ROW]
[ROW][C]Biweight[/C][C]20.245814713452[/C][C]0.11898469760827[/C][/ROW]
[ROW][C]Cosine[/C][C]20.2030834246627[/C][C]0.119538631114576[/C][/ROW]
[ROW][C]Optcosine[/C][C]20.245814713452[/C][C]0.118582491716083[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&T=3

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
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.22863435560540.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.27136564439460.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.9894269807163 & 0.123346001589881 \tabularnewline
Epanechnikov & 20.2885460022413 & 0.118312241723669 \tabularnewline
Rectangular & 21.2713656443946 & 0.133784029034183 \tabularnewline
Triangular & 19.946695691927 & 0.121705072777611 \tabularnewline
Biweight & 20.245814713452 & 0.11898469760827 \tabularnewline
Cosine & 20.2030834246627 & 0.119538631114576 \tabularnewline
Optcosine & 20.245814713452 & 0.118582491716083 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&T=4

[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]19.9894269807163[/C][C]0.123346001589881[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20.2885460022413[/C][C]0.118312241723669[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.2713656443946[/C][C]0.133784029034183[/C][/ROW]
[ROW][C]Triangular[/C][C]19.946695691927[/C][C]0.121705072777611[/C][/ROW]
[ROW][C]Biweight[/C][C]20.245814713452[/C][C]0.11898469760827[/C][/ROW]
[ROW][C]Cosine[/C][C]20.2030834246627[/C][C]0.119538631114576[/C][/ROW]
[ROW][C]Optcosine[/C][C]20.245814713452[/C][C]0.118582491716083[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&T=4

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
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.27136564439460.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.31409693318390.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.9894269807163 & 0.123346001589881 \tabularnewline
Epanechnikov & 20.2885460022413 & 0.118312241723669 \tabularnewline
Rectangular & 21.3140969331839 & 0.133784029034183 \tabularnewline
Triangular & 19.946695691927 & 0.121705072777611 \tabularnewline
Biweight & 20.245814713452 & 0.11898469760827 \tabularnewline
Cosine & 20.2030834246627 & 0.119538631114576 \tabularnewline
Optcosine & 20.245814713452 & 0.118582491716083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212153&T=5

[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]19.9894269807163[/C][C]0.123346001589881[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20.2885460022413[/C][C]0.118312241723669[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.3140969331839[/C][C]0.133784029034183[/C][/ROW]
[ROW][C]Triangular[/C][C]19.946695691927[/C][C]0.121705072777611[/C][/ROW]
[ROW][C]Biweight[/C][C]20.245814713452[/C][C]0.11898469760827[/C][/ROW]
[ROW][C]Cosine[/C][C]20.2030834246627[/C][C]0.119538631114576[/C][/ROW]
[ROW][C]Optcosine[/C][C]20.245814713452[/C][C]0.118582491716083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212153&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212153&T=5

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
Gaussian19.98942698071630.123346001589881
Epanechnikov20.28854600224130.118312241723669
Rectangular21.31409693318390.133784029034183
Triangular19.9466956919270.121705072777611
Biweight20.2458147134520.11898469760827
Cosine20.20308342466270.119538631114576
Optcosine20.2458147134520.118582491716083


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
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')
}