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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationSat, 27 Sep 2014 11:04:05 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Sep/27/t1411812312sp794y920uipalz.htm/, Retrieved Thu, 09 May 2024 21:35:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=236479, Retrieved Thu, 09 May 2024 21:35:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Consumptieprijsin...] [2014-09-20 09:19:51] [bf9bd004801723e0282da7b025e1369f]
- RMP     [Kernel Density Estimation] [] [2014-09-27 10:04:05] [beda3c52974d0e45a2203fe962302ec0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.1
101.35
101.45
101.49
101.68
101.92
102.04
102.55
104.02
105.41
105.48
105.54
105.16
105.16
105.16
105.16
105.16
105.17
105.17
105.54
106.9
107.27
107.31
107.39
107.41
107.46
113.14
117
119.28
119.39
119.5
119.67
119.67
119.73
119.77
119.77
119.78
119.78
119.78
121.28
122.44
122.72
122.75
122.8
122.81
122.83
122.83
122.83
122.84
122.85
123.61
124.74
125.1
125.29
125.45
125.51
125.55
125.57
125.81
127.41
127.75
127.76
127.8
128.23
130.01
130.07
130.17
130.21
130.22
130.23
130.23
130.23
130.23
130.24
130.13
130.14
130.79
131.38
131.61
131.72
131.89
131.89
131.96
131.99
132
132.06
132.11
132.88
135.48
136.56
136.96
137.4
138.32
138.82
138.96
138.94
139
139.19
139.22
139.37
140.74
141.17
141.51
142.94
144.81
145.41
146.11
146.23

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236479&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236479&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth4.17464169450642
#Observations108

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 4.17464169450642 \tabularnewline
#Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236479&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]4.17464169450642[/C][/ROW]
[ROW][C]#Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236479&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
Bandwidth4.17464169450642
#Observations108






Maximum Density Values
Kernelx-valuemax. density
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular125.7936823436190.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 128.128366204362 & 0.0332575124115316 \tabularnewline
Epanechnikov & 126.343019722617 & 0.0342970548628943 \tabularnewline
Rectangular & 125.793682343619 & 0.0384164885302468 \tabularnewline
Triangular & 125.656347998869 & 0.0329884283960626 \tabularnewline
Biweight & 126.617688412116 & 0.033728094485912 \tabularnewline
Cosine & 126.755022756866 & 0.033559381495645 \tabularnewline
Optcosine & 126.343019722617 & 0.0340704537942444 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236479&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]128.128366204362[/C][C]0.0332575124115316[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]126.343019722617[/C][C]0.0342970548628943[/C][/ROW]
[ROW][C]Rectangular[/C][C]125.793682343619[/C][C]0.0384164885302468[/C][/ROW]
[ROW][C]Triangular[/C][C]125.656347998869[/C][C]0.0329884283960626[/C][/ROW]
[ROW][C]Biweight[/C][C]126.617688412116[/C][C]0.033728094485912[/C][/ROW]
[ROW][C]Cosine[/C][C]126.755022756866[/C][C]0.033559381495645[/C][/ROW]
[ROW][C]Optcosine[/C][C]126.343019722617[/C][C]0.0340704537942444[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236479&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
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular125.7936823436190.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444






Maximum Density Values
Kernelx-valuemax. density
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular125.9310166883680.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 128.128366204362 & 0.0332575124115316 \tabularnewline
Epanechnikov & 126.343019722617 & 0.0342970548628943 \tabularnewline
Rectangular & 125.931016688368 & 0.0384164885302468 \tabularnewline
Triangular & 125.656347998869 & 0.0329884283960626 \tabularnewline
Biweight & 126.617688412116 & 0.033728094485912 \tabularnewline
Cosine & 126.755022756866 & 0.033559381495645 \tabularnewline
Optcosine & 126.343019722617 & 0.0340704537942444 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236479&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]128.128366204362[/C][C]0.0332575124115316[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]126.343019722617[/C][C]0.0342970548628943[/C][/ROW]
[ROW][C]Rectangular[/C][C]125.931016688368[/C][C]0.0384164885302468[/C][/ROW]
[ROW][C]Triangular[/C][C]125.656347998869[/C][C]0.0329884283960626[/C][/ROW]
[ROW][C]Biweight[/C][C]126.617688412116[/C][C]0.033728094485912[/C][/ROW]
[ROW][C]Cosine[/C][C]126.755022756866[/C][C]0.033559381495645[/C][/ROW]
[ROW][C]Optcosine[/C][C]126.343019722617[/C][C]0.0340704537942444[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236479&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
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular125.9310166883680.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444






Maximum Density Values
Kernelx-valuemax. density
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular126.0683510331180.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 128.128366204362 & 0.0332575124115316 \tabularnewline
Epanechnikov & 126.343019722617 & 0.0342970548628943 \tabularnewline
Rectangular & 126.068351033118 & 0.0384164885302468 \tabularnewline
Triangular & 125.656347998869 & 0.0329884283960626 \tabularnewline
Biweight & 126.617688412116 & 0.033728094485912 \tabularnewline
Cosine & 126.755022756866 & 0.033559381495645 \tabularnewline
Optcosine & 126.343019722617 & 0.0340704537942444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236479&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]128.128366204362[/C][C]0.0332575124115316[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]126.343019722617[/C][C]0.0342970548628943[/C][/ROW]
[ROW][C]Rectangular[/C][C]126.068351033118[/C][C]0.0384164885302468[/C][/ROW]
[ROW][C]Triangular[/C][C]125.656347998869[/C][C]0.0329884283960626[/C][/ROW]
[ROW][C]Biweight[/C][C]126.617688412116[/C][C]0.033728094485912[/C][/ROW]
[ROW][C]Cosine[/C][C]126.755022756866[/C][C]0.033559381495645[/C][/ROW]
[ROW][C]Optcosine[/C][C]126.343019722617[/C][C]0.0340704537942444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236479&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236479&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
Gaussian128.1283662043620.0332575124115316
Epanechnikov126.3430197226170.0342970548628943
Rectangular126.0683510331180.0384164885302468
Triangular125.6563479988690.0329884283960626
Biweight126.6176884121160.033728094485912
Cosine126.7550227568660.033559381495645
Optcosine126.3430197226170.0340704537942444


Figures (Output of Computation)

Input Parameters & R Code

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')
}