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Author

*Unverified author*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Wed, 14 Aug 2013 09:09:31 -0400

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/Aug/14/t1376485803so6o1kaugeeb0aa.htm/, Retrieved Sun, 05 May 2024 02:07:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211091, Retrieved Sun, 05 May 2024 02:07:51 +0000

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No (this computation is public)

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Estimated Impact

173

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

-     [Histogram] [Stap 2/2] [2013-08-14 13:02:24] [1cfd0014ba435dd2b8f9632cac0a7144]
- RMP     [Kernel Density Estimation] [dichtheidsgrafiek 2] [2013-08-14 13:09:31] [38a0db91cd47487c7649642dcb33e029] [Current]

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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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211091&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211091&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211091&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	'Gertrude Mary Cox' @ cox.wessa.net

Properties of Density Trace
Bandwidth	336.634348311313
#Observations	108

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 336.634348311313 \tabularnewline
#Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211091&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]336.634348311313[/C][/ROW]
[ROW][C]#Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211091&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211091&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	336.634348311313
#Observations	108

Maximum Density Values
Kernel	x-value	max. density
Gaussian	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9766.3317542833	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10185.8890828073 & 0.000361936796087417 \tabularnewline
Epanechnikov & 10199.0002493237 & 0.000360762903976657 \tabularnewline
Rectangular & 9766.3317542833 & 0.000381125872815769 \tabularnewline
Triangular & 10212.1114158401 & 0.000363536493236135 \tabularnewline
Biweight & 10159.6667497746 & 0.000359559344174609 \tabularnewline
Cosine & 10185.8890828073 & 0.000359979074502863 \tabularnewline
Optcosine & 10199.0002493237 & 0.000360407853821046 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211091&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]10185.8890828073[/C][C]0.000361936796087417[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10199.0002493237[/C][C]0.000360762903976657[/C][/ROW]
[ROW][C]Rectangular[/C][C]9766.3317542833[/C][C]0.000381125872815769[/C][/ROW]
[ROW][C]Triangular[/C][C]10212.1114158401[/C][C]0.000363536493236135[/C][/ROW]
[ROW][C]Biweight[/C][C]10159.6667497746[/C][C]0.000359559344174609[/C][/ROW]
[ROW][C]Cosine[/C][C]10185.8890828073[/C][C]0.000359979074502863[/C][/ROW]
[ROW][C]Optcosine[/C][C]10199.0002493237[/C][C]0.000360407853821046[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211091&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211091&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	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9766.3317542833	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

Maximum Density Values
Kernel	x-value	max. density
Gaussian	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9779.44292079967	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10185.8890828073 & 0.000361936796087417 \tabularnewline
Epanechnikov & 10199.0002493237 & 0.000360762903976657 \tabularnewline
Rectangular & 9779.44292079967 & 0.000381125872815769 \tabularnewline
Triangular & 10212.1114158401 & 0.000363536493236135 \tabularnewline
Biweight & 10159.6667497746 & 0.000359559344174609 \tabularnewline
Cosine & 10185.8890828073 & 0.000359979074502863 \tabularnewline
Optcosine & 10199.0002493237 & 0.000360407853821046 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211091&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]10185.8890828073[/C][C]0.000361936796087417[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10199.0002493237[/C][C]0.000360762903976657[/C][/ROW]
[ROW][C]Rectangular[/C][C]9779.44292079967[/C][C]0.000381125872815769[/C][/ROW]
[ROW][C]Triangular[/C][C]10212.1114158401[/C][C]0.000363536493236135[/C][/ROW]
[ROW][C]Biweight[/C][C]10159.6667497746[/C][C]0.000359559344174609[/C][/ROW]
[ROW][C]Cosine[/C][C]10185.8890828073[/C][C]0.000359979074502863[/C][/ROW]
[ROW][C]Optcosine[/C][C]10199.0002493237[/C][C]0.000360407853821046[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211091&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211091&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	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9779.44292079967	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

Maximum Density Values
Kernel	x-value	max. density
Gaussian	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9792.55408731605	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10185.8890828073 & 0.000361936796087417 \tabularnewline
Epanechnikov & 10199.0002493237 & 0.000360762903976657 \tabularnewline
Rectangular & 9792.55408731605 & 0.000381125872815769 \tabularnewline
Triangular & 10212.1114158401 & 0.000363536493236135 \tabularnewline
Biweight & 10159.6667497746 & 0.000359559344174609 \tabularnewline
Cosine & 10185.8890828073 & 0.000359979074502863 \tabularnewline
Optcosine & 10199.0002493237 & 0.000360407853821046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211091&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]10185.8890828073[/C][C]0.000361936796087417[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10199.0002493237[/C][C]0.000360762903976657[/C][/ROW]
[ROW][C]Rectangular[/C][C]9792.55408731605[/C][C]0.000381125872815769[/C][/ROW]
[ROW][C]Triangular[/C][C]10212.1114158401[/C][C]0.000363536493236135[/C][/ROW]
[ROW][C]Biweight[/C][C]10159.6667497746[/C][C]0.000359559344174609[/C][/ROW]
[ROW][C]Cosine[/C][C]10185.8890828073[/C][C]0.000359979074502863[/C][/ROW]
[ROW][C]Optcosine[/C][C]10199.0002493237[/C][C]0.000360407853821046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211091&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211091&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
Kernel	x-value	max. density
Gaussian	10185.8890828073	0.000361936796087417
Epanechnikov	10199.0002493237	0.000360762903976657
Rectangular	9792.55408731605	0.000381125872815769
Triangular	10212.1114158401	0.000363536493236135
Biweight	10159.6667497746	0.000359559344174609
Cosine	10185.8890828073	0.000359979074502863
Optcosine	10199.0002493237	0.000360407853821046

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

Postscript link

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 = 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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code