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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 computationFri, 14 Feb 2014 15:02:52 -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/14/t1392408189g71spwze5r07gyv.htm/, Retrieved Wed, 15 May 2024 11:05:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233662, Retrieved Wed, 15 May 2024 11:05:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [] [2014-02-14 20:02:52] [bc62d516d7cc59b06dcff229811e1a47] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99.7
107.5
107.5
114.5
118.7
117.8
111.7
112.3
104.9
102.4
100.3
106.6
94.2
96.9
94.7
104.9
108.3
104.7
108.3
105.2
99.2
99.3
92.3
98.6
88.4
89.5
90.5
103.5
105.1
107.1
111.6
104.6
103.3
104.6
94.1
97.7
92.4
89.5
100.1
109.6
105.5
108.9
108.8
103.9
104.3
102.1
96.6
101.4
90.4
91.8
100.4
105.3
105.1
107.6
103.7
102.7
99.2
95.6
96.3
104.1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 7 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233662&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233662&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 time7 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth2.73195685155068
#Observations60

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.73195685155068 \tabularnewline
#Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233662&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.73195685155068[/C][/ROW]
[ROW][C]#Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233662&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
Bandwidth2.73195685155068
#Observations60






Maximum Density Values
Kernelx-valuemax. density
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.6870599054090.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 104.600792608135 & 0.0600852870695227 \tabularnewline
Epanechnikov & 104.143926256772 & 0.0584814337716249 \tabularnewline
Rectangular & 103.687059905409 & 0.0598774377338877 \tabularnewline
Triangular & 104.600792608135 & 0.0601305319705837 \tabularnewline
Biweight & 104.326672797317 & 0.0585669554829028 \tabularnewline
Cosine & 104.41804606759 & 0.0587306418341796 \tabularnewline
Optcosine & 104.235299527045 & 0.0585131167078928 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233662&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]104.600792608135[/C][C]0.0600852870695227[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]104.143926256772[/C][C]0.0584814337716249[/C][/ROW]
[ROW][C]Rectangular[/C][C]103.687059905409[/C][C]0.0598774377338877[/C][/ROW]
[ROW][C]Triangular[/C][C]104.600792608135[/C][C]0.0601305319705837[/C][/ROW]
[ROW][C]Biweight[/C][C]104.326672797317[/C][C]0.0585669554829028[/C][/ROW]
[ROW][C]Cosine[/C][C]104.41804606759[/C][C]0.0587306418341796[/C][/ROW]
[ROW][C]Optcosine[/C][C]104.235299527045[/C][C]0.0585131167078928[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233662&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233662&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
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.6870599054090.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928






Maximum Density Values
Kernelx-valuemax. density
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.7784331756820.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 104.600792608135 & 0.0600852870695227 \tabularnewline
Epanechnikov & 104.143926256772 & 0.0584814337716249 \tabularnewline
Rectangular & 103.778433175682 & 0.0598774377338877 \tabularnewline
Triangular & 104.600792608135 & 0.0601305319705837 \tabularnewline
Biweight & 104.326672797317 & 0.0585669554829028 \tabularnewline
Cosine & 104.41804606759 & 0.0587306418341796 \tabularnewline
Optcosine & 104.235299527045 & 0.0585131167078928 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233662&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]104.600792608135[/C][C]0.0600852870695227[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]104.143926256772[/C][C]0.0584814337716249[/C][/ROW]
[ROW][C]Rectangular[/C][C]103.778433175682[/C][C]0.0598774377338877[/C][/ROW]
[ROW][C]Triangular[/C][C]104.600792608135[/C][C]0.0601305319705837[/C][/ROW]
[ROW][C]Biweight[/C][C]104.326672797317[/C][C]0.0585669554829028[/C][/ROW]
[ROW][C]Cosine[/C][C]104.41804606759[/C][C]0.0587306418341796[/C][/ROW]
[ROW][C]Optcosine[/C][C]104.235299527045[/C][C]0.0585131167078928[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233662&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233662&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
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.7784331756820.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928






Maximum Density Values
Kernelx-valuemax. density
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.8698064459540.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 104.600792608135 & 0.0600852870695227 \tabularnewline
Epanechnikov & 104.143926256772 & 0.0584814337716249 \tabularnewline
Rectangular & 103.869806445954 & 0.0598774377338877 \tabularnewline
Triangular & 104.600792608135 & 0.0601305319705837 \tabularnewline
Biweight & 104.326672797317 & 0.0585669554829028 \tabularnewline
Cosine & 104.41804606759 & 0.0587306418341796 \tabularnewline
Optcosine & 104.235299527045 & 0.0585131167078928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233662&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]104.600792608135[/C][C]0.0600852870695227[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]104.143926256772[/C][C]0.0584814337716249[/C][/ROW]
[ROW][C]Rectangular[/C][C]103.869806445954[/C][C]0.0598774377338877[/C][/ROW]
[ROW][C]Triangular[/C][C]104.600792608135[/C][C]0.0601305319705837[/C][/ROW]
[ROW][C]Biweight[/C][C]104.326672797317[/C][C]0.0585669554829028[/C][/ROW]
[ROW][C]Cosine[/C][C]104.41804606759[/C][C]0.0587306418341796[/C][/ROW]
[ROW][C]Optcosine[/C][C]104.235299527045[/C][C]0.0585131167078928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233662&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233662&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
Gaussian104.6007926081350.0600852870695227
Epanechnikov104.1439262567720.0584814337716249
Rectangular103.8698064459540.0598774377338877
Triangular104.6007926081350.0601305319705837
Biweight104.3266727973170.0585669554829028
Cosine104.418046067590.0587306418341796
Optcosine104.2352995270450.0585131167078928


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')
}