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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 computationMon, 14 Oct 2013 08:44:42 -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/14/t1381755073891g5ee2upuzfv4.htm/, Retrieved Sun, 28 Apr 2024 15:30:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=215523, Retrieved Sun, 28 Apr 2024 15:30:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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] [] [2013-10-14 12:44:42] [f0ec65ab0c213345bf099e498b60e56c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.93
2.02
1.85
1.77
1.81
1.67
1.55
1.62
1.79
1.73
1.77
1.95
2.08
2.26
2.02
1.9
1.97
1.76
1.93
1.91
1.96
1.99
1.98
1.96
1.95
2.26
2.07
2.02
2.07
1.88
1.75
1.78
1.87
1.94
2.03
2.13
2.04
2.18
2.02
1.99
2.09
1.88
1.8
1.77
1.85
1.9
2.03
2.02
2.09
2.3
2.16
2.02
2.31
1.98
1.74
1.82
2.07
2.04
2.07
2.13
2.14
2.43
2.26
2.11
2.19
2.04
2.04
2.05
2.08
1.98
2.07
2.12
2.15
2.35
2.19
2.17
2.3
2.09
1.95
1.89
1.95
1.98
1.95
2.06

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=215523&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=215523&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215523&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
Bandwidth0.053298205587993
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.053298205587993 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=215523&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.053298205587993[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=215523&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215523&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
Bandwidth0.053298205587993
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.024044899972912.62894832116324
Epanechnikov2.021696975836842.61551362370449
Rectangular1.998217734476222.70811307257073
Triangular2.021696975836842.63127402251067
Biweight2.017001127564722.62092858466199
Cosine2.017001127564722.62116390805639
Optcosine2.017001127564722.61687991734574

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.02404489997291 & 2.62894832116324 \tabularnewline
Epanechnikov & 2.02169697583684 & 2.61551362370449 \tabularnewline
Rectangular & 1.99821773447622 & 2.70811307257073 \tabularnewline
Triangular & 2.02169697583684 & 2.63127402251067 \tabularnewline
Biweight & 2.01700112756472 & 2.62092858466199 \tabularnewline
Cosine & 2.01700112756472 & 2.62116390805639 \tabularnewline
Optcosine & 2.01700112756472 & 2.61687991734574 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=215523&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]2.02404489997291[/C][C]2.62894832116324[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.02169697583684[/C][C]2.61551362370449[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.99821773447622[/C][C]2.70811307257073[/C][/ROW]
[ROW][C]Triangular[/C][C]2.02169697583684[/C][C]2.63127402251067[/C][/ROW]
[ROW][C]Biweight[/C][C]2.01700112756472[/C][C]2.62092858466199[/C][/ROW]
[ROW][C]Cosine[/C][C]2.01700112756472[/C][C]2.62116390805639[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.01700112756472[/C][C]2.61687991734574[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=215523&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215523&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
Gaussian2.024044899972912.62894832116324
Epanechnikov2.021696975836842.61551362370449
Rectangular1.998217734476222.70811307257073
Triangular2.021696975836842.63127402251067
Biweight2.017001127564722.62092858466199
Cosine2.017001127564722.62116390805639
Optcosine2.017001127564722.61687991734574






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.024044899972912.62894832116324
Epanechnikov2.021696975836842.61551362370449
Rectangular2.000565658612282.70811307257073
Triangular2.021696975836842.63127402251067
Biweight2.017001127564722.62092858466199
Cosine2.017001127564722.62116390805639
Optcosine2.017001127564722.61687991734574

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.02404489997291 & 2.62894832116324 \tabularnewline
Epanechnikov & 2.02169697583684 & 2.61551362370449 \tabularnewline
Rectangular & 2.00056565861228 & 2.70811307257073 \tabularnewline
Triangular & 2.02169697583684 & 2.63127402251067 \tabularnewline
Biweight & 2.01700112756472 & 2.62092858466199 \tabularnewline
Cosine & 2.01700112756472 & 2.62116390805639 \tabularnewline
Optcosine & 2.01700112756472 & 2.61687991734574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=215523&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]2.02404489997291[/C][C]2.62894832116324[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.02169697583684[/C][C]2.61551362370449[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.00056565861228[/C][C]2.70811307257073[/C][/ROW]
[ROW][C]Triangular[/C][C]2.02169697583684[/C][C]2.63127402251067[/C][/ROW]
[ROW][C]Biweight[/C][C]2.01700112756472[/C][C]2.62092858466199[/C][/ROW]
[ROW][C]Cosine[/C][C]2.01700112756472[/C][C]2.62116390805639[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.01700112756472[/C][C]2.61687991734574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=215523&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=215523&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
Gaussian2.024044899972912.62894832116324
Epanechnikov2.021696975836842.61551362370449
Rectangular2.000565658612282.70811307257073
Triangular2.021696975836842.63127402251067
Biweight2.017001127564722.62092858466199
Cosine2.017001127564722.62116390805639
Optcosine2.017001127564722.61687991734574


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')
}