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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, 04 Oct 2012 14:57:03 -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/04/t1349377101oeg1pwewytm5iw4.htm/, Retrieved Mon, 29 Apr 2024 13:34:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=172078, Retrieved Mon, 29 Apr 2024 13:34:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGemiddelde prijs van een salade Niçoise (in euro)
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] [Prijs van een sal...] [2012-10-04 18:57:03] [53258e2a15b9513ddb11a4655ef48ebf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.24
9.29
9.39
9.42
9.42
9.43
9.5
9.53
9.58
9.58
9.6
9.61
9.65
9.71
9.78
9.79
9.84
9.87
9.9
9.95
9.96
9.98
10.01
10
10.03
10.05
10.06
10.09
10.24
10.23
10.27
10.28
10.29
10.44
10.51
10.52
10.57
10.62
10.71
10.73
10.74
10.75
10.79
10.81
10.87
10.92
10.95
10.94
10.97
10.99
11.04
11.09
11.12
11.11
11.14
11.2
11.25
11.3
11.31
11.31
11.33
11.41
11.46
11.48
11.58
11.63
11.69
11.74
11.68
11.69
11.71
11.75

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'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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth0.28715617754037
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.28715617754037 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.28715617754037[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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
Bandwidth0.28715617754037
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.819883814447670.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 9.87786925369756 & 0.416892375514988 \tabularnewline
Epanechnikov & 9.81988381444767 & 0.416266338996936 \tabularnewline
Rectangular & 9.81988381444767 & 0.432833045819016 \tabularnewline
Triangular & 9.90272015623323 & 0.415014284559016 \tabularnewline
Biweight & 9.85301835116189 & 0.415387481241247 \tabularnewline
Cosine & 9.85301835116189 & 0.415352569292461 \tabularnewline
Optcosine & 9.82816744862623 & 0.415508182741362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&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]9.87786925369756[/C][C]0.416892375514988[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]9.81988381444767[/C][C]0.416266338996936[/C][/ROW]
[ROW][C]Rectangular[/C][C]9.81988381444767[/C][C]0.432833045819016[/C][/ROW]
[ROW][C]Triangular[/C][C]9.90272015623323[/C][C]0.415014284559016[/C][/ROW]
[ROW][C]Biweight[/C][C]9.85301835116189[/C][C]0.415387481241247[/C][/ROW]
[ROW][C]Cosine[/C][C]9.85301835116189[/C][C]0.415352569292461[/C][/ROW]
[ROW][C]Optcosine[/C][C]9.82816744862623[/C][C]0.415508182741362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.819883814447670.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362






Maximum Density Values
Kernelx-valuemax. density
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.828167448626230.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 9.87786925369756 & 0.416892375514988 \tabularnewline
Epanechnikov & 9.81988381444767 & 0.416266338996936 \tabularnewline
Rectangular & 9.82816744862623 & 0.432833045819016 \tabularnewline
Triangular & 9.90272015623323 & 0.415014284559016 \tabularnewline
Biweight & 9.85301835116189 & 0.415387481241247 \tabularnewline
Cosine & 9.85301835116189 & 0.415352569292461 \tabularnewline
Optcosine & 9.82816744862623 & 0.415508182741362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&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]9.87786925369756[/C][C]0.416892375514988[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]9.81988381444767[/C][C]0.416266338996936[/C][/ROW]
[ROW][C]Rectangular[/C][C]9.82816744862623[/C][C]0.432833045819016[/C][/ROW]
[ROW][C]Triangular[/C][C]9.90272015623323[/C][C]0.415014284559016[/C][/ROW]
[ROW][C]Biweight[/C][C]9.85301835116189[/C][C]0.415387481241247[/C][/ROW]
[ROW][C]Cosine[/C][C]9.85301835116189[/C][C]0.415352569292461[/C][/ROW]
[ROW][C]Optcosine[/C][C]9.82816744862623[/C][C]0.415508182741362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.828167448626230.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362






Maximum Density Values
Kernelx-valuemax. density
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.861301985340450.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 9.87786925369756 & 0.416892375514988 \tabularnewline
Epanechnikov & 9.81988381444767 & 0.416266338996936 \tabularnewline
Rectangular & 9.86130198534045 & 0.432833045819016 \tabularnewline
Triangular & 9.90272015623323 & 0.415014284559016 \tabularnewline
Biweight & 9.85301835116189 & 0.415387481241247 \tabularnewline
Cosine & 9.85301835116189 & 0.415352569292461 \tabularnewline
Optcosine & 9.82816744862623 & 0.415508182741362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&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]9.87786925369756[/C][C]0.416892375514988[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]9.81988381444767[/C][C]0.416266338996936[/C][/ROW]
[ROW][C]Rectangular[/C][C]9.86130198534045[/C][C]0.432833045819016[/C][/ROW]
[ROW][C]Triangular[/C][C]9.90272015623323[/C][C]0.415014284559016[/C][/ROW]
[ROW][C]Biweight[/C][C]9.85301835116189[/C][C]0.415387481241247[/C][/ROW]
[ROW][C]Cosine[/C][C]9.85301835116189[/C][C]0.415352569292461[/C][/ROW]
[ROW][C]Optcosine[/C][C]9.82816744862623[/C][C]0.415508182741362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.861301985340450.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362






Maximum Density Values
Kernelx-valuemax. density
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.869585619519010.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 9.87786925369756 & 0.416892375514988 \tabularnewline
Epanechnikov & 9.81988381444767 & 0.416266338996936 \tabularnewline
Rectangular & 9.86958561951901 & 0.432833045819016 \tabularnewline
Triangular & 9.90272015623323 & 0.415014284559016 \tabularnewline
Biweight & 9.85301835116189 & 0.415387481241247 \tabularnewline
Cosine & 9.85301835116189 & 0.415352569292461 \tabularnewline
Optcosine & 9.82816744862623 & 0.415508182741362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=172078&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]9.87786925369756[/C][C]0.416892375514988[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]9.81988381444767[/C][C]0.416266338996936[/C][/ROW]
[ROW][C]Rectangular[/C][C]9.86958561951901[/C][C]0.432833045819016[/C][/ROW]
[ROW][C]Triangular[/C][C]9.90272015623323[/C][C]0.415014284559016[/C][/ROW]
[ROW][C]Biweight[/C][C]9.85301835116189[/C][C]0.415387481241247[/C][/ROW]
[ROW][C]Cosine[/C][C]9.85301835116189[/C][C]0.415352569292461[/C][/ROW]
[ROW][C]Optcosine[/C][C]9.82816744862623[/C][C]0.415508182741362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=172078&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=172078&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
Gaussian9.877869253697560.416892375514988
Epanechnikov9.819883814447670.416266338996936
Rectangular9.869585619519010.432833045819016
Triangular9.902720156233230.415014284559016
Biweight9.853018351161890.415387481241247
Cosine9.853018351161890.415352569292461
Optcosine9.828167448626230.415508182741362


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')
}