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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 computationMon, 09 Dec 2013 13:47:33 -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/2013/Dec/09/t1386614876dabh7wrhqy0z9uw.htm/, Retrieved Thu, 25 Apr 2024 00:19:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231724, Retrieved Thu, 25 Apr 2024 00:19:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Percentiles] [Intrinsic Motivat...] [2010-10-12 12:10:58] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:42:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [Percentiles] [] [2011-10-18 22:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD      [Notched Boxplots] [] [2011-10-18 22:58:56] [b98453cac15ba1066b407e146608df68]
- RM D        [Back to Back Histogram] [] [2011-10-18 23:05:48] [b98453cac15ba1066b407e146608df68]
- RMPD            [Kernel Density Estimation] [] [2013-12-09 18:47:33] [02b53344bfc7e15f5310bf5039e578c4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
185
188
175
190
198
185
196
183
185
188
196
188
183
208
183
178
178
180
183
203
203
178
190
190
190
196
183
188
185
188
193
193
183
188
185
180
198
190
185
190
183
185
190
185
188
198
196
180
185
190

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231724&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]10 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=231724&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231724&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 time10 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth2.15001628891206
#Observations50

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.15001628891206 \tabularnewline
#Observations & 50 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231724&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.15001628891206[/C][/ROW]
[ROW][C]#Observations[/C][C]50[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231724&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231724&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
Bandwidth2.15001628891206
#Observations50






Maximum Density Values
Kernelx-valuemax. density
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.4249402701740.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 185.167403345969 & 0.0629278180157067 \tabularnewline
Epanechnikov & 186.514764336188 & 0.0670983734544853 \tabularnewline
Rectangular & 186.424940270174 & 0.0832452220812476 \tabularnewline
Triangular & 185.077579279954 & 0.0640603378083711 \tabularnewline
Biweight & 186.424940270174 & 0.0648066723032015 \tabularnewline
Cosine & 186.335116204159 & 0.0641657580522616 \tabularnewline
Optcosine & 186.514764336188 & 0.0663249604446936 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231724&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]185.167403345969[/C][C]0.0629278180157067[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]186.514764336188[/C][C]0.0670983734544853[/C][/ROW]
[ROW][C]Rectangular[/C][C]186.424940270174[/C][C]0.0832452220812476[/C][/ROW]
[ROW][C]Triangular[/C][C]185.077579279954[/C][C]0.0640603378083711[/C][/ROW]
[ROW][C]Biweight[/C][C]186.424940270174[/C][C]0.0648066723032015[/C][/ROW]
[ROW][C]Cosine[/C][C]186.335116204159[/C][C]0.0641657580522616[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.514764336188[/C][C]0.0663249604446936[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231724&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231724&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
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.4249402701740.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936






Maximum Density Values
Kernelx-valuemax. density
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.5147643361880.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 185.167403345969 & 0.0629278180157067 \tabularnewline
Epanechnikov & 186.514764336188 & 0.0670983734544853 \tabularnewline
Rectangular & 186.514764336188 & 0.0832452220812476 \tabularnewline
Triangular & 185.077579279954 & 0.0640603378083711 \tabularnewline
Biweight & 186.424940270174 & 0.0648066723032015 \tabularnewline
Cosine & 186.335116204159 & 0.0641657580522616 \tabularnewline
Optcosine & 186.514764336188 & 0.0663249604446936 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231724&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]185.167403345969[/C][C]0.0629278180157067[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]186.514764336188[/C][C]0.0670983734544853[/C][/ROW]
[ROW][C]Rectangular[/C][C]186.514764336188[/C][C]0.0832452220812476[/C][/ROW]
[ROW][C]Triangular[/C][C]185.077579279954[/C][C]0.0640603378083711[/C][/ROW]
[ROW][C]Biweight[/C][C]186.424940270174[/C][C]0.0648066723032015[/C][/ROW]
[ROW][C]Cosine[/C][C]186.335116204159[/C][C]0.0641657580522616[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.514764336188[/C][C]0.0663249604446936[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231724&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231724&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
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.5147643361880.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936






Maximum Density Values
Kernelx-valuemax. density
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.6045884022030.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 185.167403345969 & 0.0629278180157067 \tabularnewline
Epanechnikov & 186.514764336188 & 0.0670983734544853 \tabularnewline
Rectangular & 186.604588402203 & 0.0832452220812476 \tabularnewline
Triangular & 185.077579279954 & 0.0640603378083711 \tabularnewline
Biweight & 186.424940270174 & 0.0648066723032015 \tabularnewline
Cosine & 186.335116204159 & 0.0641657580522616 \tabularnewline
Optcosine & 186.514764336188 & 0.0663249604446936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231724&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]185.167403345969[/C][C]0.0629278180157067[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]186.514764336188[/C][C]0.0670983734544853[/C][/ROW]
[ROW][C]Rectangular[/C][C]186.604588402203[/C][C]0.0832452220812476[/C][/ROW]
[ROW][C]Triangular[/C][C]185.077579279954[/C][C]0.0640603378083711[/C][/ROW]
[ROW][C]Biweight[/C][C]186.424940270174[/C][C]0.0648066723032015[/C][/ROW]
[ROW][C]Cosine[/C][C]186.335116204159[/C][C]0.0641657580522616[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.514764336188[/C][C]0.0663249604446936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231724&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231724&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
Gaussian185.1674033459690.0629278180157067
Epanechnikov186.5147643361880.0670983734544853
Rectangular186.6045884022030.0832452220812476
Triangular185.0775792799540.0640603378083711
Biweight186.4249402701740.0648066723032015
Cosine186.3351162041590.0641657580522616
Optcosine186.5147643361880.0663249604446936


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')
}