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Author's title

Author

*Unverified author*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Tue, 12 Feb 2013 08:36:51 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Feb/12/t1360676275v9ogj4ybm1bv3di.htm/, Retrieved Sun, 28 Apr 2024 22:43:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206355, Retrieved Sun, 28 Apr 2024 22:43:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

114

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Histogram] [Economische situa...] [2013-02-05 15:31:24] [41b8d88384d696c671e043f0c3bb96a9]
- R P   [Histogram] [Economische situa...] [2013-02-12 13:33:56] [41b8d88384d696c671e043f0c3bb96a9]
- RM        [Kernel Density Estimation] [Economische situa...] [2013-02-12 13:36:51] [5d7546d7dacadccf70943ca90d1ce990] [Current]

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Dataseries X:

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Histogram

Boxplots

-48
-47
-37
-33
-30
-14
-16
-8
-14
-19
-10
-21
-17
-12
-19
-17
-15
-25
-36
-37
-22
-37
-38
-41
-38
-34
-42
-44
-47
-58
-61
-64
-67
-69
-72
-69
-69
-63
-66
-56
-63
-66
-55
-50
-46
-39
-38
-40
-33
-30
-14
-16
-10
-8
-4
-4
2
-6
-6
-7
-15
-7
-8
-10
-16
-10
-16
-17
-19
-21
-20
-19
-25
-28
-33
-43
-32
-38
-38
-31
-19
-12
-18
-21

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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=206355&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=206355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206355&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Properties of Density Trace
Bandwidth	7.23333129261483
#Observations	84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 7.23333129261483 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206355&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]7.23333129261483[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206355&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
Bandwidth	7.23333129261483
#Observations	84

Maximum Density Values
Kernel	x-value	max. density
Gaussian	-15.5864990893234	0.0208896983483723
Epanechnikov	-16.2757358080457	0.0198072538334248
Rectangular	-26.1547954430645	0.0204296153548862
Triangular	-16.9649725267679	0.0204956308760771
Biweight	-15.8162446622309	0.0201394124262376
Cosine	-15.8162446622309	0.0202583138456418
Optcosine	-16.9649725267679	0.0198971942964431

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -15.5864990893234 & 0.0208896983483723 \tabularnewline
Epanechnikov & -16.2757358080457 & 0.0198072538334248 \tabularnewline
Rectangular & -26.1547954430645 & 0.0204296153548862 \tabularnewline
Triangular & -16.9649725267679 & 0.0204956308760771 \tabularnewline
Biweight & -15.8162446622309 & 0.0201394124262376 \tabularnewline
Cosine & -15.8162446622309 & 0.0202583138456418 \tabularnewline
Optcosine & -16.9649725267679 & 0.0198971942964431 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206355&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]-15.5864990893234[/C][C]0.0208896983483723[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-16.2757358080457[/C][C]0.0198072538334248[/C][/ROW]
[ROW][C]Rectangular[/C][C]-26.1547954430645[/C][C]0.0204296153548862[/C][/ROW]
[ROW][C]Triangular[/C][C]-16.9649725267679[/C][C]0.0204956308760771[/C][/ROW]
[ROW][C]Biweight[/C][C]-15.8162446622309[/C][C]0.0201394124262376[/C][/ROW]
[ROW][C]Cosine[/C][C]-15.8162446622309[/C][C]0.0202583138456418[/C][/ROW]
[ROW][C]Optcosine[/C][C]-16.9649725267679[/C][C]0.0198971942964431[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206355&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
Kernel	x-value	max. density
Gaussian	-15.5864990893234	0.0208896983483723
Epanechnikov	-16.2757358080457	0.0198072538334248
Rectangular	-26.1547954430645	0.0204296153548862
Triangular	-16.9649725267679	0.0204956308760771
Biweight	-15.8162446622309	0.0201394124262376
Cosine	-15.8162446622309	0.0202583138456418
Optcosine	-16.9649725267679	0.0198971942964431

Maximum Density Values
Kernel	x-value	max. density
Gaussian	-15.5864990893234	0.0208896983483723
Epanechnikov	-16.2757358080457	0.0198072538334248
Rectangular	-25.9250498701571	0.0204296153548862
Triangular	-16.9649725267679	0.0204956308760771
Biweight	-15.8162446622309	0.0201394124262376
Cosine	-15.8162446622309	0.0202583138456418
Optcosine	-16.9649725267679	0.0198971942964431

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -15.5864990893234 & 0.0208896983483723 \tabularnewline
Epanechnikov & -16.2757358080457 & 0.0198072538334248 \tabularnewline
Rectangular & -25.9250498701571 & 0.0204296153548862 \tabularnewline
Triangular & -16.9649725267679 & 0.0204956308760771 \tabularnewline
Biweight & -15.8162446622309 & 0.0201394124262376 \tabularnewline
Cosine & -15.8162446622309 & 0.0202583138456418 \tabularnewline
Optcosine & -16.9649725267679 & 0.0198971942964431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206355&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]-15.5864990893234[/C][C]0.0208896983483723[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-16.2757358080457[/C][C]0.0198072538334248[/C][/ROW]
[ROW][C]Rectangular[/C][C]-25.9250498701571[/C][C]0.0204296153548862[/C][/ROW]
[ROW][C]Triangular[/C][C]-16.9649725267679[/C][C]0.0204956308760771[/C][/ROW]
[ROW][C]Biweight[/C][C]-15.8162446622309[/C][C]0.0201394124262376[/C][/ROW]
[ROW][C]Cosine[/C][C]-15.8162446622309[/C][C]0.0202583138456418[/C][/ROW]
[ROW][C]Optcosine[/C][C]-16.9649725267679[/C][C]0.0198971942964431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206355&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
Kernel	x-value	max. density
Gaussian	-15.5864990893234	0.0208896983483723
Epanechnikov	-16.2757358080457	0.0198072538334248
Rectangular	-25.9250498701571	0.0204296153548862
Triangular	-16.9649725267679	0.0204956308760771
Biweight	-15.8162446622309	0.0201394124262376
Cosine	-15.8162446622309	0.0202583138456418
Optcosine	-16.9649725267679	0.0198971942964431

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

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Figure 3

PNG link

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PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 8 ; par2 = grey ; par3 = TRUE ; par4 = Interval/Ratio ;

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')
}

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code