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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, 29 Sep 2012 09:05:50 -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/2012/Sep/29/t1348924008i0a70ukh1i5ydzk.htm/, Retrieved Thu, 02 May 2024 17:09:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=170449, Retrieved Thu, 02 May 2024 17:09:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [] [2012-09-23 14:20:58] [73ff502f5cc0e8f9d4cad04b672b43dc]
- RMPD    [Kernel Density Estimation] [] [2012-09-29 13:05:50] [19a5fa3cc9952272699ac0aa748608b8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.6
2
2.6
3
2.6
2.9
2.5
2.4
1.5
1.1
0.6
0.9
1.1
1.5
1.7
1.2
0.4
-0.7
-1.4
-1.6
-1.2
-0.4
-0.2
-0.3
-0.5
0
-0.5
0.2
0.7
1.6
2.6
3.3
3.3
3.2
3.5
3.9
4.5
4.6
6.6
7.1
8.9
8.8
8.5
7.6
7.5
7.5
6.1
6.3
8.4
7.1
5.6
4.2
2.1
1.2
0.9
1.4
1.7
1.7
1.9
1.3
-0.7
0.3
0.8
0.9
1.1
2.5
2.7
3.3
4.2
3.8
3.8
3.2
2.9
1.9
1.7
1.6
1.7
1.2
0.7
-0.2
-1.5
-1.2
-1
0
-0.6
0.7
1.3
0.8
1
0.5
0.3
1
1
1.1
1.5
1.5
2
1.7
0.6
1.2
1.5
2.1
3.2
3.9
4.6
4.2
4.4
3.7
3.7
2.8
2.9
3.9
3.1
3
2.8
2.4
2.1
3.1
3
3.1
3.3
3.3
3.8
3.1
3.9
4
4.4
3.7
3.6
3.4
2.8
2.8
2.6
3.3
2.4
1.6
0.7
0
-1.1
-1.2
-1.3
-1.6
-1.3
-1.6
-1.1
-1
0.3
1.2
0.7
1.1
2.1
2.5
2.3
2.3
2.6
3.2
2.2
2.7
2.2
1.4
2.4
2
1.3
1.1
1.4
1.8
1.9
1.6

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'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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170449&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170449&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'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth0.554375068383324
#Observations168

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.554375068383324 \tabularnewline
#Observations & 168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170449&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.554375068383324[/C][/ROW]
[ROW][C]#Observations[/C][C]168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170449&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
Bandwidth0.554375068383324
#Observations168






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular1.904807922770360.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.52600654166625 & 0.214653362594733 \tabularnewline
Epanechnikov & 1.71540723221831 & 0.213335442427692 \tabularnewline
Rectangular & 1.90480792277036 & 0.213867845923048 \tabularnewline
Triangular & 1.60717826618856 & 0.214153010652801 \tabularnewline
Biweight & 1.634235507696 & 0.212821885586376 \tabularnewline
Cosine & 1.634235507696 & 0.212944400047656 \tabularnewline
Optcosine & 1.68834999071087 & 0.213065031201122 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170449&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]1.52600654166625[/C][C]0.214653362594733[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.71540723221831[/C][C]0.213335442427692[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.90480792277036[/C][C]0.213867845923048[/C][/ROW]
[ROW][C]Triangular[/C][C]1.60717826618856[/C][C]0.214153010652801[/C][/ROW]
[ROW][C]Biweight[/C][C]1.634235507696[/C][C]0.212821885586376[/C][/ROW]
[ROW][C]Cosine[/C][C]1.634235507696[/C][C]0.212944400047656[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.68834999071087[/C][C]0.213065031201122[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170449&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
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular1.904807922770360.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular2.01303688880010.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.52600654166625 & 0.214653362594733 \tabularnewline
Epanechnikov & 1.71540723221831 & 0.213335442427692 \tabularnewline
Rectangular & 2.0130368888001 & 0.213867845923048 \tabularnewline
Triangular & 1.60717826618856 & 0.214153010652801 \tabularnewline
Biweight & 1.634235507696 & 0.212821885586376 \tabularnewline
Cosine & 1.634235507696 & 0.212944400047656 \tabularnewline
Optcosine & 1.68834999071087 & 0.213065031201122 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170449&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]1.52600654166625[/C][C]0.214653362594733[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.71540723221831[/C][C]0.213335442427692[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.0130368888001[/C][C]0.213867845923048[/C][/ROW]
[ROW][C]Triangular[/C][C]1.60717826618856[/C][C]0.214153010652801[/C][/ROW]
[ROW][C]Biweight[/C][C]1.634235507696[/C][C]0.212821885586376[/C][/ROW]
[ROW][C]Cosine[/C][C]1.634235507696[/C][C]0.212944400047656[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.68834999071087[/C][C]0.213065031201122[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170449&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170449&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
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular2.01303688880010.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular2.391838269904210.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.52600654166625 & 0.214653362594733 \tabularnewline
Epanechnikov & 1.71540723221831 & 0.213335442427692 \tabularnewline
Rectangular & 2.39183826990421 & 0.213867845923048 \tabularnewline
Triangular & 1.60717826618856 & 0.214153010652801 \tabularnewline
Biweight & 1.634235507696 & 0.212821885586376 \tabularnewline
Cosine & 1.634235507696 & 0.212944400047656 \tabularnewline
Optcosine & 1.68834999071087 & 0.213065031201122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170449&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]1.52600654166625[/C][C]0.214653362594733[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.71540723221831[/C][C]0.213335442427692[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.39183826990421[/C][C]0.213867845923048[/C][/ROW]
[ROW][C]Triangular[/C][C]1.60717826618856[/C][C]0.214153010652801[/C][/ROW]
[ROW][C]Biweight[/C][C]1.634235507696[/C][C]0.212821885586376[/C][/ROW]
[ROW][C]Cosine[/C][C]1.634235507696[/C][C]0.212944400047656[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.68834999071087[/C][C]0.213065031201122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170449&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170449&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
Gaussian1.526006541666250.214653362594733
Epanechnikov1.715407232218310.213335442427692
Rectangular2.391838269904210.213867845923048
Triangular1.607178266188560.214153010652801
Biweight1.6342355076960.212821885586376
Cosine1.6342355076960.212944400047656
Optcosine1.688349990710870.213065031201122


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')
}