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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 computationMon, 22 Oct 2012 15:21:16 -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/2012/Oct/22/t1350934110wqseyga0icehqzg.htm/, Retrieved Fri, 03 May 2024 15:05:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=182199, Retrieved Fri, 03 May 2024 15:05:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact37

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] [] [2012-10-22 19:21:16] [712f2f4436a9b7aba1a90edc9e618eb7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,1
7,9
7,9
8,3
8,6
8,7
8,5
8,3
8
8
8,8
8,7
8,5
8,1
7,8
7,7
7,5
7,2
6,9
6,6
6,5
6,6
7,7
8
7,7
7,2
7
7
7,3
7,3
7,1
6,9
6,7
6,8
7,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182199&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182199&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth0.244706344423595
#Observations79

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.244706344423595 \tabularnewline
#Observations & 79 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182199&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.244706344423595[/C][/ROW]
[ROW][C]#Observations[/C][C]79[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182199&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
Bandwidth0.244706344423595
#Observations79






Maximum Density Values
Kernelx-valuemax. density
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.69063213887080.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 7.95165683188318 & 0.581630888305365 \tabularnewline
Epanechnikov & 7.9108717236 & 0.548871794665454 \tabularnewline
Rectangular & 7.6906321388708 & 0.582373578499561 \tabularnewline
Triangular & 7.99244194016637 & 0.57265429264987 \tabularnewline
Biweight & 7.93534278856991 & 0.556820809272711 \tabularnewline
Cosine & 7.93534278856991 & 0.560617189785002 \tabularnewline
Optcosine & 7.9108717236 & 0.550364028534787 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182199&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]7.95165683188318[/C][C]0.581630888305365[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]7.9108717236[/C][C]0.548871794665454[/C][/ROW]
[ROW][C]Rectangular[/C][C]7.6906321388708[/C][C]0.582373578499561[/C][/ROW]
[ROW][C]Triangular[/C][C]7.99244194016637[/C][C]0.57265429264987[/C][/ROW]
[ROW][C]Biweight[/C][C]7.93534278856991[/C][C]0.556820809272711[/C][/ROW]
[ROW][C]Cosine[/C][C]7.93534278856991[/C][C]0.560617189785002[/C][/ROW]
[ROW][C]Optcosine[/C][C]7.9108717236[/C][C]0.550364028534787[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182199&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182199&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
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.69063213887080.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787






Maximum Density Values
Kernelx-valuemax. density
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.698789160527430.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 7.95165683188318 & 0.581630888305365 \tabularnewline
Epanechnikov & 7.9108717236 & 0.548871794665454 \tabularnewline
Rectangular & 7.69878916052743 & 0.582373578499561 \tabularnewline
Triangular & 7.99244194016637 & 0.57265429264987 \tabularnewline
Biweight & 7.93534278856991 & 0.556820809272711 \tabularnewline
Cosine & 7.93534278856991 & 0.560617189785002 \tabularnewline
Optcosine & 7.9108717236 & 0.550364028534787 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182199&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]7.95165683188318[/C][C]0.581630888305365[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]7.9108717236[/C][C]0.548871794665454[/C][/ROW]
[ROW][C]Rectangular[/C][C]7.69878916052743[/C][C]0.582373578499561[/C][/ROW]
[ROW][C]Triangular[/C][C]7.99244194016637[/C][C]0.57265429264987[/C][/ROW]
[ROW][C]Biweight[/C][C]7.93534278856991[/C][C]0.556820809272711[/C][/ROW]
[ROW][C]Cosine[/C][C]7.93534278856991[/C][C]0.560617189785002[/C][/ROW]
[ROW][C]Optcosine[/C][C]7.9108717236[/C][C]0.550364028534787[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182199&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182199&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
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.698789160527430.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787






Maximum Density Values
Kernelx-valuemax. density
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.706946182184070.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 7.95165683188318 & 0.581630888305365 \tabularnewline
Epanechnikov & 7.9108717236 & 0.548871794665454 \tabularnewline
Rectangular & 7.70694618218407 & 0.582373578499561 \tabularnewline
Triangular & 7.99244194016637 & 0.57265429264987 \tabularnewline
Biweight & 7.93534278856991 & 0.556820809272711 \tabularnewline
Cosine & 7.93534278856991 & 0.560617189785002 \tabularnewline
Optcosine & 7.9108717236 & 0.550364028534787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182199&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]7.95165683188318[/C][C]0.581630888305365[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]7.9108717236[/C][C]0.548871794665454[/C][/ROW]
[ROW][C]Rectangular[/C][C]7.70694618218407[/C][C]0.582373578499561[/C][/ROW]
[ROW][C]Triangular[/C][C]7.99244194016637[/C][C]0.57265429264987[/C][/ROW]
[ROW][C]Biweight[/C][C]7.93534278856991[/C][C]0.556820809272711[/C][/ROW]
[ROW][C]Cosine[/C][C]7.93534278856991[/C][C]0.560617189785002[/C][/ROW]
[ROW][C]Optcosine[/C][C]7.9108717236[/C][C]0.550364028534787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182199&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182199&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
Gaussian7.951656831883180.581630888305365
Epanechnikov7.91087172360.548871794665454
Rectangular7.706946182184070.582373578499561
Triangular7.992441940166370.57265429264987
Biweight7.935342788569910.556820809272711
Cosine7.935342788569910.560617189785002
Optcosine7.91087172360.550364028534787


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):
par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}