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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 computationTue, 25 Sep 2012 15:00:11 -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/25/t1348599662snroukvwr5644hr.htm/, Retrieved Thu, 02 May 2024 00:35:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169976, Retrieved Thu, 02 May 2024 00:35:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184

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] [Gemiddelde consum...] [2012-09-18 17:20:52] [a5b8e09850dc0947000b5c91d678d658]
- RMPD    [Kernel Density Estimation] [Dichtheidsgrafiek...] [2012-09-25 19:00:11] [d083c6d046cc71723436dadeef11a810] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
79.49
79.69
79.86
79.87
79.83
79.83
79.83
79.37
79.53
79.78
79.94
79.97
79.97
79.98
80.25
80.38
80.13
80.15
80.15
80.18
80.47
80.83
80.62
80.66
80.66
80.67
80.8
81.04
81.24
81.26
81.26
81.47
81.94
82.83
82.29
82.32
82.32
82.3
82.54
82.54
82.62
82.63
82.63
82.63
82.71
83.25
83.14
83.34
83.34
83.37
83.33
83.26
83.66
83.64
83.64
83.71
83.87
84.17
84.35
84.44
84.44
84.45
84.67
84.95
84.89
84.93
84.93
84.93
85.45
85.77
85.79
85.9

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&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'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth0.739763645424126
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.739763645424126 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.739763645424126[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&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
Bandwidth0.739763645424126
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.32751946908310.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 80.2201947932265 & 0.19004733359201 \tabularnewline
Epanechnikov & 80.3275194690831 & 0.178618212318636 \tabularnewline
Rectangular & 80.3275194690831 & 0.173433853655189 \tabularnewline
Triangular & 80.1557999877125 & 0.183060996831541 \tabularnewline
Biweight & 80.2845895987404 & 0.181763173819606 \tabularnewline
Cosine & 80.2631246635691 & 0.182839145172435 \tabularnewline
Optcosine & 80.3060545339117 & 0.17954791400777 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&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]80.2201947932265[/C][C]0.19004733359201[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]80.3275194690831[/C][C]0.178618212318636[/C][/ROW]
[ROW][C]Rectangular[/C][C]80.3275194690831[/C][C]0.173433853655189[/C][/ROW]
[ROW][C]Triangular[/C][C]80.1557999877125[/C][C]0.183060996831541[/C][/ROW]
[ROW][C]Biweight[/C][C]80.2845895987404[/C][C]0.181763173819606[/C][/ROW]
[ROW][C]Cosine[/C][C]80.2631246635691[/C][C]0.182839145172435[/C][/ROW]
[ROW][C]Optcosine[/C][C]80.3060545339117[/C][C]0.17954791400777[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&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
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.32751946908310.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777






Maximum Density Values
Kernelx-valuemax. density
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.34898440425440.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 80.2201947932265 & 0.19004733359201 \tabularnewline
Epanechnikov & 80.3275194690831 & 0.178618212318636 \tabularnewline
Rectangular & 80.3489844042544 & 0.173433853655189 \tabularnewline
Triangular & 80.1557999877125 & 0.183060996831541 \tabularnewline
Biweight & 80.2845895987404 & 0.181763173819606 \tabularnewline
Cosine & 80.2631246635691 & 0.182839145172435 \tabularnewline
Optcosine & 80.3060545339117 & 0.17954791400777 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&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]80.2201947932265[/C][C]0.19004733359201[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]80.3275194690831[/C][C]0.178618212318636[/C][/ROW]
[ROW][C]Rectangular[/C][C]80.3489844042544[/C][C]0.173433853655189[/C][/ROW]
[ROW][C]Triangular[/C][C]80.1557999877125[/C][C]0.183060996831541[/C][/ROW]
[ROW][C]Biweight[/C][C]80.2845895987404[/C][C]0.181763173819606[/C][/ROW]
[ROW][C]Cosine[/C][C]80.2631246635691[/C][C]0.182839145172435[/C][/ROW]
[ROW][C]Optcosine[/C][C]80.3060545339117[/C][C]0.17954791400777[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&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
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.34898440425440.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777






Maximum Density Values
Kernelx-valuemax. density
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.4563090801110.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 80.2201947932265 & 0.19004733359201 \tabularnewline
Epanechnikov & 80.3275194690831 & 0.178618212318636 \tabularnewline
Rectangular & 80.456309080111 & 0.173433853655189 \tabularnewline
Triangular & 80.1557999877125 & 0.183060996831541 \tabularnewline
Biweight & 80.2845895987404 & 0.181763173819606 \tabularnewline
Cosine & 80.2631246635691 & 0.182839145172435 \tabularnewline
Optcosine & 80.3060545339117 & 0.17954791400777 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&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]80.2201947932265[/C][C]0.19004733359201[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]80.3275194690831[/C][C]0.178618212318636[/C][/ROW]
[ROW][C]Rectangular[/C][C]80.456309080111[/C][C]0.173433853655189[/C][/ROW]
[ROW][C]Triangular[/C][C]80.1557999877125[/C][C]0.183060996831541[/C][/ROW]
[ROW][C]Biweight[/C][C]80.2845895987404[/C][C]0.181763173819606[/C][/ROW]
[ROW][C]Cosine[/C][C]80.2631246635691[/C][C]0.182839145172435[/C][/ROW]
[ROW][C]Optcosine[/C][C]80.3060545339117[/C][C]0.17954791400777[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&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
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.4563090801110.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777






Maximum Density Values
Kernelx-valuemax. density
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.47777401528230.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 80.2201947932265 & 0.19004733359201 \tabularnewline
Epanechnikov & 80.3275194690831 & 0.178618212318636 \tabularnewline
Rectangular & 80.4777740152823 & 0.173433853655189 \tabularnewline
Triangular & 80.1557999877125 & 0.183060996831541 \tabularnewline
Biweight & 80.2845895987404 & 0.181763173819606 \tabularnewline
Cosine & 80.2631246635691 & 0.182839145172435 \tabularnewline
Optcosine & 80.3060545339117 & 0.17954791400777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169976&T=5

[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]80.2201947932265[/C][C]0.19004733359201[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]80.3275194690831[/C][C]0.178618212318636[/C][/ROW]
[ROW][C]Rectangular[/C][C]80.4777740152823[/C][C]0.173433853655189[/C][/ROW]
[ROW][C]Triangular[/C][C]80.1557999877125[/C][C]0.183060996831541[/C][/ROW]
[ROW][C]Biweight[/C][C]80.2845895987404[/C][C]0.181763173819606[/C][/ROW]
[ROW][C]Cosine[/C][C]80.2631246635691[/C][C]0.182839145172435[/C][/ROW]
[ROW][C]Optcosine[/C][C]80.3060545339117[/C][C]0.17954791400777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169976&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169976&T=5

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
Gaussian80.22019479322650.19004733359201
Epanechnikov80.32751946908310.178618212318636
Rectangular80.47777401528230.173433853655189
Triangular80.15579998771250.183060996831541
Biweight80.28458959874040.181763173819606
Cosine80.26312466356910.182839145172435
Optcosine80.30605453391170.17954791400777


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')
}