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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationWed, 23 Oct 2013 18:23:34 -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/2013/Oct/23/t13825670512noi0q3vr7ep29o.htm/, Retrieved Sun, 28 Apr 2024 04:58:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=219220, Retrieved Sun, 28 Apr 2024 04:58:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Tukey lambda PPCC Plot] [Intrinsic Motivat...] [2010-10-12 12:09:04] [b98453cac15ba1066b407e146608df68]
- RMPD    [Kernel Density Estimation] [Gaussian kernel d...] [2013-10-23 22:23:34] [12aa97dfde985f95a295900f01959e26] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
16
19
18
16
23
17
12
19
16
19
20
13
20
27
17
8
25
26
13
19
15
5
16
14
24
24
9
19
19
25
19
18
15
12
21
12
15
28
25
19
20
24
26
25
12
12
15
17
14
16
11
20
11
22
20
19
17
21
23
18
17
27
25
19
22
24
20
19
11
22
22
16
20
24
16
16
22
24
16
27
11
21
20
20
27
20
12
8
21
18
24
16
18
20
20
19
17
16
26
15
22
17
23
21
19
14
17
12
24
18
20
16
20
22
12
16
17
22
12
14
23
15
17
28
20
23
13
18
23
19
23
12
16
23
13
22
18
23
20
10
17
18
15
23
17
17
22
20
20
19
18
22
20
22
18
16
16
16
16
17
18

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth1.44414956238819
#Observations162

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.44414956238819 \tabularnewline
#Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.44414956238819[/C][/ROW]
[ROW][C]#Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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
Bandwidth1.44414956238819
#Observations162






Maximum Density Values
Kernelx-valuemax. density
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.64638082470660.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 18.575878790685 & 0.0873272859104555 \tabularnewline
Epanechnikov & 18.018180011098 & 0.090081210596422 \tabularnewline
Rectangular & 17.6463808247066 & 0.0962446931339478 \tabularnewline
Triangular & 18.018180011098 & 0.0885877411019416 \tabularnewline
Biweight & 18.018180011098 & 0.0887830039458377 \tabularnewline
Cosine & 18.1421130732284 & 0.0883255214193907 \tabularnewline
Optcosine & 18.018180011098 & 0.0897287431652344 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&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]18.575878790685[/C][C]0.0873272859104555[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]18.018180011098[/C][C]0.090081210596422[/C][/ROW]
[ROW][C]Rectangular[/C][C]17.6463808247066[/C][C]0.0962446931339478[/C][/ROW]
[ROW][C]Triangular[/C][C]18.018180011098[/C][C]0.0885877411019416[/C][/ROW]
[ROW][C]Biweight[/C][C]18.018180011098[/C][C]0.0887830039458377[/C][/ROW]
[ROW][C]Cosine[/C][C]18.1421130732284[/C][C]0.0883255214193907[/C][/ROW]
[ROW][C]Optcosine[/C][C]18.018180011098[/C][C]0.0897287431652344[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.64638082470660.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344






Maximum Density Values
Kernelx-valuemax. density
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.77031388683710.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 18.575878790685 & 0.0873272859104555 \tabularnewline
Epanechnikov & 18.018180011098 & 0.090081210596422 \tabularnewline
Rectangular & 17.7703138868371 & 0.0962446931339478 \tabularnewline
Triangular & 18.018180011098 & 0.0885877411019416 \tabularnewline
Biweight & 18.018180011098 & 0.0887830039458377 \tabularnewline
Cosine & 18.1421130732284 & 0.0883255214193907 \tabularnewline
Optcosine & 18.018180011098 & 0.0897287431652344 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&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]18.575878790685[/C][C]0.0873272859104555[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]18.018180011098[/C][C]0.090081210596422[/C][/ROW]
[ROW][C]Rectangular[/C][C]17.7703138868371[/C][C]0.0962446931339478[/C][/ROW]
[ROW][C]Triangular[/C][C]18.018180011098[/C][C]0.0885877411019416[/C][/ROW]
[ROW][C]Biweight[/C][C]18.018180011098[/C][C]0.0887830039458377[/C][/ROW]
[ROW][C]Cosine[/C][C]18.1421130732284[/C][C]0.0883255214193907[/C][/ROW]
[ROW][C]Optcosine[/C][C]18.018180011098[/C][C]0.0897287431652344[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.77031388683710.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344






Maximum Density Values
Kernelx-valuemax. density
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.83228041790230.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 18.575878790685 & 0.0873272859104555 \tabularnewline
Epanechnikov & 18.018180011098 & 0.090081210596422 \tabularnewline
Rectangular & 17.8322804179023 & 0.0962446931339478 \tabularnewline
Triangular & 18.018180011098 & 0.0885877411019416 \tabularnewline
Biweight & 18.018180011098 & 0.0887830039458377 \tabularnewline
Cosine & 18.1421130732284 & 0.0883255214193907 \tabularnewline
Optcosine & 18.018180011098 & 0.0897287431652344 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&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]18.575878790685[/C][C]0.0873272859104555[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]18.018180011098[/C][C]0.090081210596422[/C][/ROW]
[ROW][C]Rectangular[/C][C]17.8322804179023[/C][C]0.0962446931339478[/C][/ROW]
[ROW][C]Triangular[/C][C]18.018180011098[/C][C]0.0885877411019416[/C][/ROW]
[ROW][C]Biweight[/C][C]18.018180011098[/C][C]0.0887830039458377[/C][/ROW]
[ROW][C]Cosine[/C][C]18.1421130732284[/C][C]0.0883255214193907[/C][/ROW]
[ROW][C]Optcosine[/C][C]18.018180011098[/C][C]0.0897287431652344[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular17.83228041790230.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344






Maximum Density Values
Kernelx-valuemax. density
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular18.14211307322840.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 18.575878790685 & 0.0873272859104555 \tabularnewline
Epanechnikov & 18.018180011098 & 0.090081210596422 \tabularnewline
Rectangular & 18.1421130732284 & 0.0962446931339478 \tabularnewline
Triangular & 18.018180011098 & 0.0885877411019416 \tabularnewline
Biweight & 18.018180011098 & 0.0887830039458377 \tabularnewline
Cosine & 18.1421130732284 & 0.0883255214193907 \tabularnewline
Optcosine & 18.018180011098 & 0.0897287431652344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219220&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]18.575878790685[/C][C]0.0873272859104555[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]18.018180011098[/C][C]0.090081210596422[/C][/ROW]
[ROW][C]Rectangular[/C][C]18.1421130732284[/C][C]0.0962446931339478[/C][/ROW]
[ROW][C]Triangular[/C][C]18.018180011098[/C][C]0.0885877411019416[/C][/ROW]
[ROW][C]Biweight[/C][C]18.018180011098[/C][C]0.0887830039458377[/C][/ROW]
[ROW][C]Cosine[/C][C]18.1421130732284[/C][C]0.0883255214193907[/C][/ROW]
[ROW][C]Optcosine[/C][C]18.018180011098[/C][C]0.0897287431652344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219220&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219220&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
Gaussian18.5758787906850.0873272859104555
Epanechnikov18.0181800110980.090081210596422
Rectangular18.14211307322840.0962446931339478
Triangular18.0181800110980.0885877411019416
Biweight18.0181800110980.0887830039458377
Cosine18.14211307322840.0883255214193907
Optcosine18.0181800110980.0897287431652344


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 8 ; par2 = 0 ;
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')
}