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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 13:45:59 -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/t1360694777gjjk01dfu51spp9.htm/, Retrieved Mon, 29 Apr 2024 01:53:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206433, Retrieved Mon, 29 Apr 2024 01:53:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-     [Univariate Data Series] [Gemiddelde prijs ...] [2013-02-05 20:51:41] [e8e05c89adf74c738414cf9a446b974e]
- RMPD    [Kernel Density Estimation] [] [2013-02-12 18:45:59] [8e6f8740463a1fe0a9188e5ce9dc522d] [Current]

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Dataseries X:

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Histogram

Boxplots

1.01
1.02
1.04
1.06
1.06
1.06
1.06
1.06
1.02
0.98
0.99
0.99
0.94
0.96
0.98
1.01
1.01
1.02
1.04
1.03
1.05
1.08
1.17
1.11
1.11
1.11
1.2
1.21
1.31
1.37
1.37
1.26
1.23
1.17
1.06
0.95
0.92
0.92
0.9
0.93
0.93
0.97
0.96
0.99
0.98
0.96
1
0.99
1.03
1.02
1.07
1.13
1.15
1.16
1.14
1.15
1.15
1.16
1.17
1.22
1.26
1.29
1.36
1.38
1.37
1.37
1.37
1.36
1.38
1.4
1.44
1.42

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=206433&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=206433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206433&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	0.0579096414132606
#Observations	72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0579096414132606 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206433&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0579096414132606[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206433&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	0.0579096414132606
#Observations	72

Maximum Density Values
Kernel	x-value	max. density
Gaussian	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.01282791528884	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.01630133152555 & 2.93268967500376 \tabularnewline
Epanechnikov & 1.0145646234072 & 2.8135711109963 \tabularnewline
Rectangular & 1.01282791528884 & 2.83863701505543 \tabularnewline
Triangular & 1.01977474776227 & 2.87775465669613 \tabularnewline
Biweight & 1.01977474776227 & 2.85246582537744 \tabularnewline
Cosine & 1.01977474776227 & 2.86651016894966 \tabularnewline
Optcosine & 1.02151145588062 & 2.82418894221215 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206433&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]1.01630133152555[/C][C]2.93268967500376[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.0145646234072[/C][C]2.8135711109963[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.01282791528884[/C][C]2.83863701505543[/C][/ROW]
[ROW][C]Triangular[/C][C]1.01977474776227[/C][C]2.87775465669613[/C][/ROW]
[ROW][C]Biweight[/C][C]1.01977474776227[/C][C]2.85246582537744[/C][/ROW]
[ROW][C]Cosine[/C][C]1.01977474776227[/C][C]2.86651016894966[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.02151145588062[/C][C]2.82418894221215[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206433&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206433&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	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.01282791528884	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

Maximum Density Values
Kernel	x-value	max. density
Gaussian	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.0145646234072	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.01630133152555 & 2.93268967500376 \tabularnewline
Epanechnikov & 1.0145646234072 & 2.8135711109963 \tabularnewline
Rectangular & 1.0145646234072 & 2.83863701505543 \tabularnewline
Triangular & 1.01977474776227 & 2.87775465669613 \tabularnewline
Biweight & 1.01977474776227 & 2.85246582537744 \tabularnewline
Cosine & 1.01977474776227 & 2.86651016894966 \tabularnewline
Optcosine & 1.02151145588062 & 2.82418894221215 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206433&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]1.01630133152555[/C][C]2.93268967500376[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.0145646234072[/C][C]2.8135711109963[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.0145646234072[/C][C]2.83863701505543[/C][/ROW]
[ROW][C]Triangular[/C][C]1.01977474776227[/C][C]2.87775465669613[/C][/ROW]
[ROW][C]Biweight[/C][C]1.01977474776227[/C][C]2.85246582537744[/C][/ROW]
[ROW][C]Cosine[/C][C]1.01977474776227[/C][C]2.86651016894966[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.02151145588062[/C][C]2.82418894221215[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206433&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206433&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	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.0145646234072	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

Maximum Density Values
Kernel	x-value	max. density
Gaussian	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.07534940754964	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.01630133152555 & 2.93268967500376 \tabularnewline
Epanechnikov & 1.0145646234072 & 2.8135711109963 \tabularnewline
Rectangular & 1.07534940754964 & 2.83863701505543 \tabularnewline
Triangular & 1.01977474776227 & 2.87775465669613 \tabularnewline
Biweight & 1.01977474776227 & 2.85246582537744 \tabularnewline
Cosine & 1.01977474776227 & 2.86651016894966 \tabularnewline
Optcosine & 1.02151145588062 & 2.82418894221215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206433&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]1.01630133152555[/C][C]2.93268967500376[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.0145646234072[/C][C]2.8135711109963[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.07534940754964[/C][C]2.83863701505543[/C][/ROW]
[ROW][C]Triangular[/C][C]1.01977474776227[/C][C]2.87775465669613[/C][/ROW]
[ROW][C]Biweight[/C][C]1.01977474776227[/C][C]2.85246582537744[/C][/ROW]
[ROW][C]Cosine[/C][C]1.01977474776227[/C][C]2.86651016894966[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.02151145588062[/C][C]2.82418894221215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206433&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206433&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	1.01630133152555	2.93268967500376
Epanechnikov	1.0145646234072	2.8135711109963
Rectangular	1.07534940754964	2.83863701505543
Triangular	1.01977474776227	2.87775465669613
Biweight	1.01977474776227	2.85246582537744
Cosine	1.01977474776227	2.86651016894966
Optcosine	1.02151145588062	2.82418894221215

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

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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