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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 computationSat, 27 Sep 2014 13:36:02 +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/2014/Sep/27/t14118215469ff543n2ivftt69.htm/, Retrieved Fri, 10 May 2024 17:59:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=236523, Retrieved Fri, 10 May 2024 17:59:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [] [2014-09-27 12:36:02] [deb17a426e61079f456ada9a85a82a78] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.5
1.6
1.8
1.5
1.3
1.6
1.6
1.8
1.8
1.6
1.8
2
1.3
1.1
1
1.2
1.2
1.3
1.3
1.4
1.1
0.9
1
1.1
1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.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=236523&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.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=236523&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236523&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.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
Bandwidth0.241002128900687
#Observations108

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.241002128900687 \tabularnewline
#Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236523&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.241002128900687[/C][/ROW]
[ROW][C]#Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236523&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236523&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
Bandwidth0.241002128900687
#Observations108






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.713050918121540.548565190518557
Epanechnikov1.704350306040510.538099185453858
Rectangular1.895763771823080.576724081673373
Triangular1.608643573149230.541748481136813
Biweight1.739152754364620.540102800045259
Cosine1.721751530202560.541552514949202
Optcosine1.704350306040510.537876627484956

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.71305091812154 & 0.548565190518557 \tabularnewline
Epanechnikov & 1.70435030604051 & 0.538099185453858 \tabularnewline
Rectangular & 1.89576377182308 & 0.576724081673373 \tabularnewline
Triangular & 1.60864357314923 & 0.541748481136813 \tabularnewline
Biweight & 1.73915275436462 & 0.540102800045259 \tabularnewline
Cosine & 1.72175153020256 & 0.541552514949202 \tabularnewline
Optcosine & 1.70435030604051 & 0.537876627484956 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236523&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]1.71305091812154[/C][C]0.548565190518557[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.70435030604051[/C][C]0.538099185453858[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.89576377182308[/C][C]0.576724081673373[/C][/ROW]
[ROW][C]Triangular[/C][C]1.60864357314923[/C][C]0.541748481136813[/C][/ROW]
[ROW][C]Biweight[/C][C]1.73915275436462[/C][C]0.540102800045259[/C][/ROW]
[ROW][C]Cosine[/C][C]1.72175153020256[/C][C]0.541552514949202[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.70435030604051[/C][C]0.537876627484956[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236523&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236523&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
Gaussian1.713050918121540.548565190518557
Epanechnikov1.704350306040510.538099185453858
Rectangular1.895763771823080.576724081673373
Triangular1.608643573149230.541748481136813
Biweight1.739152754364620.540102800045259
Cosine1.721751530202560.541552514949202
Optcosine1.704350306040510.537876627484956






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.713050918121540.548565190518557
Epanechnikov1.704350306040510.538099185453858
Rectangular1.90446438390410.576724081673373
Triangular1.608643573149230.541748481136813
Biweight1.739152754364620.540102800045259
Cosine1.721751530202560.541552514949202
Optcosine1.704350306040510.537876627484956

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.71305091812154 & 0.548565190518557 \tabularnewline
Epanechnikov & 1.70435030604051 & 0.538099185453858 \tabularnewline
Rectangular & 1.9044643839041 & 0.576724081673373 \tabularnewline
Triangular & 1.60864357314923 & 0.541748481136813 \tabularnewline
Biweight & 1.73915275436462 & 0.540102800045259 \tabularnewline
Cosine & 1.72175153020256 & 0.541552514949202 \tabularnewline
Optcosine & 1.70435030604051 & 0.537876627484956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236523&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]1.71305091812154[/C][C]0.548565190518557[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.70435030604051[/C][C]0.538099185453858[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.9044643839041[/C][C]0.576724081673373[/C][/ROW]
[ROW][C]Triangular[/C][C]1.60864357314923[/C][C]0.541748481136813[/C][/ROW]
[ROW][C]Biweight[/C][C]1.73915275436462[/C][C]0.540102800045259[/C][/ROW]
[ROW][C]Cosine[/C][C]1.72175153020256[/C][C]0.541552514949202[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.70435030604051[/C][C]0.537876627484956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236523&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236523&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
Gaussian1.713050918121540.548565190518557
Epanechnikov1.704350306040510.538099185453858
Rectangular1.90446438390410.576724081673373
Triangular1.608643573149230.541748481136813
Biweight1.739152754364620.540102800045259
Cosine1.721751530202560.541552514949202
Optcosine1.704350306040510.537876627484956


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')
}