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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, 30 Sep 2014 14:03:10 +0100

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/2014/Sep/30/t14120822855dfl3iy08kuwg3l.htm/, Retrieved Fri, 10 May 2024 09:29:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=236997, Retrieved Fri, 10 May 2024 09:29:02 +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] [] [2014-09-28 18:43:41] [5ec968f6342c3a2f2357137b8ba7cfaf]
- R PD  [Univariate Data Series] [] [2014-09-28 18:49:56] [5ec968f6342c3a2f2357137b8ba7cfaf]
- RMPD      [Kernel Density Estimation] [] [2014-09-30 13:03:10] [fc9e02cb2d6d14d0c83d12e3a82852a5] [Current]

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Dataseries X:

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Histogram

Boxplots

6
1.5
5.7
16.7
11.1
6.7
12
11.2
11.3
15.7
8.8
4.7
3.4
-2.8
3
-6.7
-10.4
-8.7
-14.7
-21.8
-26
-28.4
-26.7
-26.2
-32.7
-32.8
-37.1
-36.3
-32.2
-36
-30.6
-23.6
-16.3
-32.4
-25.8
-23.1
-17.4
-10.5
-7.8
1.7
4.6
-6.4
-0.1
-3.3
1.9
2.5
1.2
1.6
0.8
4.9
-2.2
2.3
-3.6
-3.8
-3.9
-3.3
-15.8
-18.4
-19.5
-21.6
-23
-22.2
-19.4
-17.2
-18.5
-11.1
-13.6
-17.4
-14.5
-15.2
-8.1
-3.9
-5.2
-9.7
-15.7
-20.2
-15
-16.9
-21.6
-10.8
-12.1
-3
-7.8
-6.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236997&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]3 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=236997&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236997&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Properties of Density Trace
Bandwidth	4.96889595742325
#Observations	84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 4.96889595742325 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236997&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]4.96889595742325[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236997&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236997&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	4.96889595742325
#Observations	84

Maximum Density Values
Kernel	x-value	max. density
Gaussian	-2.91860035101369	0.0242239023383268
Epanechnikov	-2.75497339260951	0.0243725640890139
Rectangular	-11.099948271223	0.026245766617676
Triangular	-3.73673514303463	0.0244266031793832
Biweight	-2.91860035101369	0.0242229515462233
Cosine	-3.08222730941788	0.0242044086384584
Optcosine	-2.59134643420532	0.0242882569574822

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -2.91860035101369 & 0.0242239023383268 \tabularnewline
Epanechnikov & -2.75497339260951 & 0.0243725640890139 \tabularnewline
Rectangular & -11.099948271223 & 0.026245766617676 \tabularnewline
Triangular & -3.73673514303463 & 0.0244266031793832 \tabularnewline
Biweight & -2.91860035101369 & 0.0242229515462233 \tabularnewline
Cosine & -3.08222730941788 & 0.0242044086384584 \tabularnewline
Optcosine & -2.59134643420532 & 0.0242882569574822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236997&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]-2.91860035101369[/C][C]0.0242239023383268[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-2.75497339260951[/C][C]0.0243725640890139[/C][/ROW]
[ROW][C]Rectangular[/C][C]-11.099948271223[/C][C]0.026245766617676[/C][/ROW]
[ROW][C]Triangular[/C][C]-3.73673514303463[/C][C]0.0244266031793832[/C][/ROW]
[ROW][C]Biweight[/C][C]-2.91860035101369[/C][C]0.0242229515462233[/C][/ROW]
[ROW][C]Cosine[/C][C]-3.08222730941788[/C][C]0.0242044086384584[/C][/ROW]
[ROW][C]Optcosine[/C][C]-2.59134643420532[/C][C]0.0242882569574822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236997&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236997&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	-2.91860035101369	0.0242239023383268
Epanechnikov	-2.75497339260951	0.0243725640890139
Rectangular	-11.099948271223	0.026245766617676
Triangular	-3.73673514303463	0.0244266031793832
Biweight	-2.91860035101369	0.0242229515462233
Cosine	-3.08222730941788	0.0242044086384584
Optcosine	-2.59134643420532	0.0242882569574822

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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