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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 18:35:41 -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/t13825677508zpi2xw7uelm9yv.htm/, Retrieved Sun, 28 Apr 2024 06:51:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=219223, Retrieved Sun, 28 Apr 2024 06:51:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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] [] [2013-10-23 22:35:41] [12aa97dfde985f95a295900f01959e26] [Current]
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Dataset

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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth0.971168750326297
#Observations162

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.971168750326297 \tabularnewline
#Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.971168750326297[/C][/ROW]
[ROW][C]#Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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
Bandwidth0.971168750326297
#Observations162






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.38054482659870.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.7743781680362 & 0.114228588468764 \tabularnewline
Epanechnikov & 22.4271730311035 & 0.116574488608823 \tabularnewline
Rectangular & 22.3805448265987 & 0.139448309962117 \tabularnewline
Triangular & 22.0075191905602 & 0.118115992001026 \tabularnewline
Biweight & 22.1007755995698 & 0.114814958791457 \tabularnewline
Cosine & 22.054147395065 & 0.114658854281611 \tabularnewline
Optcosine & 22.4271730311035 & 0.11549377954715 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&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]21.7743781680362[/C][C]0.114228588468764[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.4271730311035[/C][C]0.116574488608823[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.3805448265987[/C][C]0.139448309962117[/C][/ROW]
[ROW][C]Triangular[/C][C]22.0075191905602[/C][C]0.118115992001026[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1007755995698[/C][C]0.114814958791457[/C][/ROW]
[ROW][C]Cosine[/C][C]22.054147395065[/C][C]0.114658854281611[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.4271730311035[/C][C]0.11549377954715[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.38054482659870.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.42717303110350.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.7743781680362 & 0.114228588468764 \tabularnewline
Epanechnikov & 22.4271730311035 & 0.116574488608823 \tabularnewline
Rectangular & 22.4271730311035 & 0.139448309962117 \tabularnewline
Triangular & 22.0075191905602 & 0.118115992001026 \tabularnewline
Biweight & 22.1007755995698 & 0.114814958791457 \tabularnewline
Cosine & 22.054147395065 & 0.114658854281611 \tabularnewline
Optcosine & 22.4271730311035 & 0.11549377954715 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&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]21.7743781680362[/C][C]0.114228588468764[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.4271730311035[/C][C]0.116574488608823[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.4271730311035[/C][C]0.139448309962117[/C][/ROW]
[ROW][C]Triangular[/C][C]22.0075191905602[/C][C]0.118115992001026[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1007755995698[/C][C]0.114814958791457[/C][/ROW]
[ROW][C]Cosine[/C][C]22.054147395065[/C][C]0.114658854281611[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.4271730311035[/C][C]0.11549377954715[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.42717303110350.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.56705764461790.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.7743781680362 & 0.114228588468764 \tabularnewline
Epanechnikov & 22.4271730311035 & 0.116574488608823 \tabularnewline
Rectangular & 22.5670576446179 & 0.139448309962117 \tabularnewline
Triangular & 22.0075191905602 & 0.118115992001026 \tabularnewline
Biweight & 22.1007755995698 & 0.114814958791457 \tabularnewline
Cosine & 22.054147395065 & 0.114658854281611 \tabularnewline
Optcosine & 22.4271730311035 & 0.11549377954715 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&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]21.7743781680362[/C][C]0.114228588468764[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.4271730311035[/C][C]0.116574488608823[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.5670576446179[/C][C]0.139448309962117[/C][/ROW]
[ROW][C]Triangular[/C][C]22.0075191905602[/C][C]0.118115992001026[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1007755995698[/C][C]0.114814958791457[/C][/ROW]
[ROW][C]Cosine[/C][C]22.054147395065[/C][C]0.114658854281611[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.4271730311035[/C][C]0.11549377954715[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.56705764461790.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.61368584912280.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.7743781680362 & 0.114228588468764 \tabularnewline
Epanechnikov & 22.4271730311035 & 0.116574488608823 \tabularnewline
Rectangular & 22.6136858491228 & 0.139448309962117 \tabularnewline
Triangular & 22.0075191905602 & 0.118115992001026 \tabularnewline
Biweight & 22.1007755995698 & 0.114814958791457 \tabularnewline
Cosine & 22.054147395065 & 0.114658854281611 \tabularnewline
Optcosine & 22.4271730311035 & 0.11549377954715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=219223&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]21.7743781680362[/C][C]0.114228588468764[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.4271730311035[/C][C]0.116574488608823[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.6136858491228[/C][C]0.139448309962117[/C][/ROW]
[ROW][C]Triangular[/C][C]22.0075191905602[/C][C]0.118115992001026[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1007755995698[/C][C]0.114814958791457[/C][/ROW]
[ROW][C]Cosine[/C][C]22.054147395065[/C][C]0.114658854281611[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.4271730311035[/C][C]0.11549377954715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=219223&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=219223&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
Gaussian21.77437816803620.114228588468764
Epanechnikov22.42717303110350.116574488608823
Rectangular22.61368584912280.139448309962117
Triangular22.00751919056020.118115992001026
Biweight22.10077559956980.114814958791457
Cosine22.0541473950650.114658854281611
Optcosine22.42717303110350.11549377954715


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')
}