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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 computationSun, 09 Feb 2014 05:51:02 -0500
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/Feb/09/t1391943175dmtlxsumh6sq3r0.htm/, Retrieved Thu, 16 May 2024 13:26:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233397, Retrieved Thu, 16 May 2024 13:26:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [] [2014-02-01 15:35:49] [43d51d95d0fd856e5acb4054b3243aca]
- RMPD    [Kernel Density Estimation] [] [2014-02-09 10:51:02] [5f7d0cda5d8a9348873c82369b6851b6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
28.33
28.67
28.81
28.99
29.16
29.25
29.25
29.38
29.48
29.65
29.69
29.73
29.81
30.05
30.29
30.37
30.5
30.67
30.76
30.84
30.86
31.09
31.2
31.19
31.18
31.31
31.39
31.39
31.37
31.36
31.37
31.35
31.34
31.47
31.48
31.54
31.55
31.55
31.57
31.66
31.74
31.78
31.8
31.68
31.7
31.7
31.75
31.73
31.82
31.9
31.82
31.51
31.42
30.97
30.99
30.92
30.95
30.82
30.72
30.73

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 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 & 8 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233397&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]8 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=233397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233397&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 time8 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth0.353155397883381
#Observations60

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.353155397883381 \tabularnewline
#Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233397&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.353155397883381[/C][/ROW]
[ROW][C]#Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233397&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
Bandwidth0.353155397883381
#Observations60






Maximum Density Values
Kernelx-valuemax. density
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.23386047930270.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 31.4342534009689 & 0.552588834523039 \tabularnewline
Epanechnikov & 31.3451898802283 & 0.543567930032095 \tabularnewline
Rectangular & 31.2338604793027 & 0.57219171907744 \tabularnewline
Triangular & 31.3897216405986 & 0.548763948929345 \tabularnewline
Biweight & 31.378588700506 & 0.542722662910206 \tabularnewline
Cosine & 31.3897216405986 & 0.543413461334036 \tabularnewline
Optcosine & 31.3563228203209 & 0.54275500810895 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233397&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]31.4342534009689[/C][C]0.552588834523039[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]31.3451898802283[/C][C]0.543567930032095[/C][/ROW]
[ROW][C]Rectangular[/C][C]31.2338604793027[/C][C]0.57219171907744[/C][/ROW]
[ROW][C]Triangular[/C][C]31.3897216405986[/C][C]0.548763948929345[/C][/ROW]
[ROW][C]Biweight[/C][C]31.378588700506[/C][C]0.542722662910206[/C][/ROW]
[ROW][C]Cosine[/C][C]31.3897216405986[/C][C]0.543413461334036[/C][/ROW]
[ROW][C]Optcosine[/C][C]31.3563228203209[/C][C]0.54275500810895[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233397&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
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.23386047930270.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895






Maximum Density Values
Kernelx-valuemax. density
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.24499341939530.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 31.4342534009689 & 0.552588834523039 \tabularnewline
Epanechnikov & 31.3451898802283 & 0.543567930032095 \tabularnewline
Rectangular & 31.2449934193953 & 0.57219171907744 \tabularnewline
Triangular & 31.3897216405986 & 0.548763948929345 \tabularnewline
Biweight & 31.378588700506 & 0.542722662910206 \tabularnewline
Cosine & 31.3897216405986 & 0.543413461334036 \tabularnewline
Optcosine & 31.3563228203209 & 0.54275500810895 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233397&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]31.4342534009689[/C][C]0.552588834523039[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]31.3451898802283[/C][C]0.543567930032095[/C][/ROW]
[ROW][C]Rectangular[/C][C]31.2449934193953[/C][C]0.57219171907744[/C][/ROW]
[ROW][C]Triangular[/C][C]31.3897216405986[/C][C]0.548763948929345[/C][/ROW]
[ROW][C]Biweight[/C][C]31.378588700506[/C][C]0.542722662910206[/C][/ROW]
[ROW][C]Cosine[/C][C]31.3897216405986[/C][C]0.543413461334036[/C][/ROW]
[ROW][C]Optcosine[/C][C]31.3563228203209[/C][C]0.54275500810895[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233397&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233397&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
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.24499341939530.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895






Maximum Density Values
Kernelx-valuemax. density
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.25612635948780.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 31.4342534009689 & 0.552588834523039 \tabularnewline
Epanechnikov & 31.3451898802283 & 0.543567930032095 \tabularnewline
Rectangular & 31.2561263594878 & 0.57219171907744 \tabularnewline
Triangular & 31.3897216405986 & 0.548763948929345 \tabularnewline
Biweight & 31.378588700506 & 0.542722662910206 \tabularnewline
Cosine & 31.3897216405986 & 0.543413461334036 \tabularnewline
Optcosine & 31.3563228203209 & 0.54275500810895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233397&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]31.4342534009689[/C][C]0.552588834523039[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]31.3451898802283[/C][C]0.543567930032095[/C][/ROW]
[ROW][C]Rectangular[/C][C]31.2561263594878[/C][C]0.57219171907744[/C][/ROW]
[ROW][C]Triangular[/C][C]31.3897216405986[/C][C]0.548763948929345[/C][/ROW]
[ROW][C]Biweight[/C][C]31.378588700506[/C][C]0.542722662910206[/C][/ROW]
[ROW][C]Cosine[/C][C]31.3897216405986[/C][C]0.543413461334036[/C][/ROW]
[ROW][C]Optcosine[/C][C]31.3563228203209[/C][C]0.54275500810895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233397&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233397&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
Gaussian31.43425340096890.552588834523039
Epanechnikov31.34518988022830.543567930032095
Rectangular31.25612635948780.57219171907744
Triangular31.38972164059860.548763948929345
Biweight31.3785887005060.542722662910206
Cosine31.38972164059860.543413461334036
Optcosine31.35632282032090.54275500810895


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')
}