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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, 28 Sep 2013 12:53:32 -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/Sep/28/t1380387240ppieykmv6y3qeev.htm/, Retrieved Mon, 29 Apr 2024 09:44:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212354, Retrieved Mon, 29 Apr 2024 09:44:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

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] [Weekly copies sol...] [2013-09-21 22:05:29] [c3a2ef029354d13f314aaba7e04fbc3f]
- RMP     [Kernel Density Estimation] [Wekelijkse verkoc...] [2013-09-28 16:53:32] [74a92a9d3a2c9c03f2186ea574174bd1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
189.561
184.439
182.985
183.828
184.036
183.214
183.464
173.718
180.210
171.252
172.705
174.006
172.043
169.445
169.449
177.073
170.799
171.648
172.220
165.795
167.466
165.528
162.851
165.864
162.094
162.385
164.293
165.983
159.680
161.739
159.302
167.795
164.242
159.743
160.887
163.844
161.172
159.330
155.570
156.749
155.012
163.419
153.630
154.535
151.543
152.955
150.166
151.416
150.332
152.196
153.422
147.435

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212354&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212354&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'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth4.09074877950482
#Observations52

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 4.09074877950482 \tabularnewline
#Observations & 52 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212354&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]4.09074877950482[/C][/ROW]
[ROW][C]#Observations[/C][C]52[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212354&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
Bandwidth4.09074877950482
#Observations52






Maximum Density Values
Kernelx-valuemax. density
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular165.9538226864930.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 163.605351320179 & 0.0355394033974033 \tabularnewline
Epanechnikov & 165.692881423569 & 0.0351327734435108 \tabularnewline
Rectangular & 165.953822686493 & 0.0379980452156562 \tabularnewline
Triangular & 164.257704477488 & 0.0351044434111797 \tabularnewline
Biweight & 165.04052826626 & 0.0348842938455694 \tabularnewline
Cosine & 164.649116371874 & 0.034920069980933 \tabularnewline
Optcosine & 165.692881423569 & 0.0350290250973785 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212354&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]163.605351320179[/C][C]0.0355394033974033[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]165.692881423569[/C][C]0.0351327734435108[/C][/ROW]
[ROW][C]Rectangular[/C][C]165.953822686493[/C][C]0.0379980452156562[/C][/ROW]
[ROW][C]Triangular[/C][C]164.257704477488[/C][C]0.0351044434111797[/C][/ROW]
[ROW][C]Biweight[/C][C]165.04052826626[/C][C]0.0348842938455694[/C][/ROW]
[ROW][C]Cosine[/C][C]164.649116371874[/C][C]0.034920069980933[/C][/ROW]
[ROW][C]Optcosine[/C][C]165.692881423569[/C][C]0.0350290250973785[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212354&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212354&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
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular165.9538226864930.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785






Maximum Density Values
Kernelx-valuemax. density
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular166.0842933179550.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 163.605351320179 & 0.0355394033974033 \tabularnewline
Epanechnikov & 165.692881423569 & 0.0351327734435108 \tabularnewline
Rectangular & 166.084293317955 & 0.0379980452156562 \tabularnewline
Triangular & 164.257704477488 & 0.0351044434111797 \tabularnewline
Biweight & 165.04052826626 & 0.0348842938455694 \tabularnewline
Cosine & 164.649116371874 & 0.034920069980933 \tabularnewline
Optcosine & 165.692881423569 & 0.0350290250973785 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212354&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]163.605351320179[/C][C]0.0355394033974033[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]165.692881423569[/C][C]0.0351327734435108[/C][/ROW]
[ROW][C]Rectangular[/C][C]166.084293317955[/C][C]0.0379980452156562[/C][/ROW]
[ROW][C]Triangular[/C][C]164.257704477488[/C][C]0.0351044434111797[/C][/ROW]
[ROW][C]Biweight[/C][C]165.04052826626[/C][C]0.0348842938455694[/C][/ROW]
[ROW][C]Cosine[/C][C]164.649116371874[/C][C]0.034920069980933[/C][/ROW]
[ROW][C]Optcosine[/C][C]165.692881423569[/C][C]0.0350290250973785[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212354&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212354&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
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular166.0842933179550.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785






Maximum Density Values
Kernelx-valuemax. density
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular166.2147639494170.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 163.605351320179 & 0.0355394033974033 \tabularnewline
Epanechnikov & 165.692881423569 & 0.0351327734435108 \tabularnewline
Rectangular & 166.214763949417 & 0.0379980452156562 \tabularnewline
Triangular & 164.257704477488 & 0.0351044434111797 \tabularnewline
Biweight & 165.04052826626 & 0.0348842938455694 \tabularnewline
Cosine & 164.649116371874 & 0.034920069980933 \tabularnewline
Optcosine & 165.692881423569 & 0.0350290250973785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212354&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]163.605351320179[/C][C]0.0355394033974033[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]165.692881423569[/C][C]0.0351327734435108[/C][/ROW]
[ROW][C]Rectangular[/C][C]166.214763949417[/C][C]0.0379980452156562[/C][/ROW]
[ROW][C]Triangular[/C][C]164.257704477488[/C][C]0.0351044434111797[/C][/ROW]
[ROW][C]Biweight[/C][C]165.04052826626[/C][C]0.0348842938455694[/C][/ROW]
[ROW][C]Cosine[/C][C]164.649116371874[/C][C]0.034920069980933[/C][/ROW]
[ROW][C]Optcosine[/C][C]165.692881423569[/C][C]0.0350290250973785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212354&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212354&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
Gaussian163.6053513201790.0355394033974033
Epanechnikov165.6928814235690.0351327734435108
Rectangular166.2147639494170.0379980452156562
Triangular164.2577044774880.0351044434111797
Biweight165.040528266260.0348842938455694
Cosine164.6491163718740.034920069980933
Optcosine165.6928814235690.0350290250973785


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')
}