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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 computationSun, 14 Dec 2014 12:34:16 +0000
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/Dec/14/t1418560556zlo1ljf3zbp6ry1.htm/, Retrieved Thu, 16 May 2024 11:35:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267512, Retrieved Thu, 16 May 2024 11:35:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [2.3 Kernel Densit...] [2014-12-14 12:34:16] [d784cae208306d5933987ca1a74122e8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.913425
-4.08657
3.95844
1.91343
6.91343
7.91343
-0.0865746
4.95844
-1.08657
-12.0416
-0.041565
6.91343
-1.61389
4.91343
1.38611
-0.041565
-1.08657
1.91343
2.91343
-3.04156
-0.041565
4.95844
-0.0865746
-3.04156
-5.08657
-0.0865746
6.91343
-3.04156
1.91343
6.95844
7.91343
-1.04156
-0.041565
-0.041565
-3.04156
-3.04156
-3.04156
-3.08657
0.913425
-7.08657
0.958435
-4.04156
2.95844
4.38611
-3.04156
-2.6589
2.3411
-2.6589
-6.08657
-8.04156
-6.08657
-2.61389
-1.08657
-0.0865746
-3.04156
-4.08657
0.38611
-4.04156
1.38611
-3.04156
-1.04156
5.95844
-0.658899
1.38611
-3.61389
-1.08657
2.91343
6.91343
5.3411
2.95844
-1.08657
5.91343
-2.04156
2.95844
3.95844
-4.61389
0.913425
-6.04156
1.38611
-1.61389
2.38611
-0.041565
-4.04156
-1.6589
-4.6589
-0.658899
3.38611
0.958435
-3.6589
2.38611
2.91343
2.3411
-3.08657
5.3411
-2.08657
0.38611
-4.04156
0.958435
7.38611
0.38611
-1.6589
-6.04156
1.38611
1.91343
6.38611
4.95844
3.3411
-1.61389
-0.658899
1.91343
-3.61389
-2.08657
0.958435
3.3411
2.95844
-1.6589
3.91343
5.3411
0.38611
-3.6589
4.3411
6.95844
2.91343
5.91343
-5.08657
-6.08657
5.95844
5.91343
-1.61389
-3.61389
-3.6589
3.95844
-0.0865746
-0.658899
-5.04156
4.95844
-3.6589
-5.08657
3.3411
0.913425
-6.04156
-1.6589
-4.08657
1.3411
0.341101
3.95844
2.95844
1.91343
-9.61389
-3.6589
3.3411
6.95844
-7.08657
3.38611
0.341101
3.38611
-0.61389
-7.6589
4.3411
2.91343
-0.0865746
-2.61389
-3.04156
-6.6589
-8.04156
-0.041565
-0.658899
-1.6589
-5.08657
-2.08657
-5.08657
-10.0866
0.341101
-1.6589
6.38611
4.3411
0.38611
4.38611
-1.6589
-6.6589
1.91343
3.3411
5.91343
1.91343
-1.6589
5.95844
2.91343
0.913425
5.3411
0.38611
-4.6589
0.341101
4.91343
-2.08657
-0.041565
2.3411
0.341101
-3.61389
2.38611
1.3411
-2.08657
-1.08657
-5.08657
-0.61389
-1.6589
-4.61389
0.341101

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'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=267512&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=267512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267512&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth1.2207736971879
#Observations207

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.2207736971879 \tabularnewline
#Observations & 207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267512&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.2207736971879[/C][/ROW]
[ROW][C]#Observations[/C][C]207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267512&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
Bandwidth1.2207736971879
#Observations207






Maximum Density Values
Kernelx-valuemax. density
Gaussian-0.0621521098487730.0935631161523569
Epanechnikov-0.0621521098487730.0916456657205241
Rectangular-1.663698421969760.0971007968305014
Triangular0.3115420296461210.092864295672437
Biweight-0.2756916181315710.0920363520295931
Cosine-0.1689218639901710.0922799595545114
Optcosine-0.0621521098487730.0915794701047392

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -0.062152109848773 & 0.0935631161523569 \tabularnewline
Epanechnikov & -0.062152109848773 & 0.0916456657205241 \tabularnewline
Rectangular & -1.66369842196976 & 0.0971007968305014 \tabularnewline
Triangular & 0.311542029646121 & 0.092864295672437 \tabularnewline
Biweight & -0.275691618131571 & 0.0920363520295931 \tabularnewline
Cosine & -0.168921863990171 & 0.0922799595545114 \tabularnewline
Optcosine & -0.062152109848773 & 0.0915794701047392 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267512&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]-0.062152109848773[/C][C]0.0935631161523569[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-0.062152109848773[/C][C]0.0916456657205241[/C][/ROW]
[ROW][C]Rectangular[/C][C]-1.66369842196976[/C][C]0.0971007968305014[/C][/ROW]
[ROW][C]Triangular[/C][C]0.311542029646121[/C][C]0.092864295672437[/C][/ROW]
[ROW][C]Biweight[/C][C]-0.275691618131571[/C][C]0.0920363520295931[/C][/ROW]
[ROW][C]Cosine[/C][C]-0.168921863990171[/C][C]0.0922799595545114[/C][/ROW]
[ROW][C]Optcosine[/C][C]-0.062152109848773[/C][C]0.0915794701047392[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267512&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267512&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
Gaussian-0.0621521098487730.0935631161523569
Epanechnikov-0.0621521098487730.0916456657205241
Rectangular-1.663698421969760.0971007968305014
Triangular0.3115420296461210.092864295672437
Biweight-0.2756916181315710.0920363520295931
Cosine-0.1689218639901710.0922799595545114
Optcosine-0.0621521098487730.0915794701047392






Maximum Density Values
Kernelx-valuemax. density
Gaussian-0.0621521098487730.0935631161523569
Epanechnikov-0.0621521098487730.0916456657205241
Rectangular-1.610313544899060.0971007968305014
Triangular0.3115420296461210.092864295672437
Biweight-0.2756916181315710.0920363520295931
Cosine-0.1689218639901710.0922799595545114
Optcosine-0.0621521098487730.0915794701047392

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -0.062152109848773 & 0.0935631161523569 \tabularnewline
Epanechnikov & -0.062152109848773 & 0.0916456657205241 \tabularnewline
Rectangular & -1.61031354489906 & 0.0971007968305014 \tabularnewline
Triangular & 0.311542029646121 & 0.092864295672437 \tabularnewline
Biweight & -0.275691618131571 & 0.0920363520295931 \tabularnewline
Cosine & -0.168921863990171 & 0.0922799595545114 \tabularnewline
Optcosine & -0.062152109848773 & 0.0915794701047392 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267512&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]-0.062152109848773[/C][C]0.0935631161523569[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-0.062152109848773[/C][C]0.0916456657205241[/C][/ROW]
[ROW][C]Rectangular[/C][C]-1.61031354489906[/C][C]0.0971007968305014[/C][/ROW]
[ROW][C]Triangular[/C][C]0.311542029646121[/C][C]0.092864295672437[/C][/ROW]
[ROW][C]Biweight[/C][C]-0.275691618131571[/C][C]0.0920363520295931[/C][/ROW]
[ROW][C]Cosine[/C][C]-0.168921863990171[/C][C]0.0922799595545114[/C][/ROW]
[ROW][C]Optcosine[/C][C]-0.062152109848773[/C][C]0.0915794701047392[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267512&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267512&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
Gaussian-0.0621521098487730.0935631161523569
Epanechnikov-0.0621521098487730.0916456657205241
Rectangular-1.610313544899060.0971007968305014
Triangular0.3115420296461210.092864295672437
Biweight-0.2756916181315710.0920363520295931
Cosine-0.1689218639901710.0922799595545114
Optcosine-0.0621521098487730.0915794701047392


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')
}