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Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationSun, 22 Dec 2013 08:39:23 -0500
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/Dec/22/t1387719626d5gjfvea9nl469m.htm/, Retrieved Sun, 05 Dec 2021 17:12:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232520, Retrieved Sun, 05 Dec 2021 17:12:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [] [2013-12-22 13:39:23] [20efb5145ec2a2ddd8dcd418764211fa] [Current]
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Dataseries X:
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 12 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232520&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232520&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=0

As an alternative you can also use a 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 time12 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







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=232520&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=232520&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=1

As an alternative you can also use a 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=232520&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=232520&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=2

As an alternative you can also use a 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=232520&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=232520&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=3

As an alternative you can also use a 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=232520&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=232520&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=4

As an alternative you can also use a 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=232520&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=232520&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232520&T=5

As an alternative you can also use a 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



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')
}