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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 computationMon, 02 Feb 2015 13:29:29 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Feb/02/t1422883780nh4nc6hgc52ah8u.htm/, Retrieved Sat, 18 May 2024 00:06:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=276474, Retrieved Sat, 18 May 2024 00:06:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGlenn Waem
Estimated Impact53

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] [] [2015-02-02 13:29:29] [3d92bf785db8aeb0f2ab1bed7b74f49c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116
118
116
111
108
102
102
129
136
137
126
119
117
120
116
110
104
98
98
124
130
131
121
114
111

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Properties of Density Trace
Bandwidth4.68074795943487
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 4.68074795943487 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]4.68074795943487[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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
Bandwidth4.68074795943487
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.2768660190620.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 108.516524272099 & 0.0281711933124125 \tabularnewline
Epanechnikov & 111.848763494973 & 0.0281369548052213 \tabularnewline
Rectangular & 113.276866019062 & 0.0293680307075646 \tabularnewline
Triangular & 108.992558446795 & 0.0282913033948106 \tabularnewline
Biweight & 111.055373203812 & 0.0279034049660726 \tabularnewline
Cosine & 110.261982912652 & 0.0278774004500197 \tabularnewline
Optcosine & 111.690085436741 & 0.0280785510295003 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&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]108.516524272099[/C][C]0.0281711933124125[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]111.848763494973[/C][C]0.0281369548052213[/C][/ROW]
[ROW][C]Rectangular[/C][C]113.276866019062[/C][C]0.0293680307075646[/C][/ROW]
[ROW][C]Triangular[/C][C]108.992558446795[/C][C]0.0282913033948106[/C][/ROW]
[ROW][C]Biweight[/C][C]111.055373203812[/C][C]0.0279034049660726[/C][/ROW]
[ROW][C]Cosine[/C][C]110.261982912652[/C][C]0.0278774004500197[/C][/ROW]
[ROW][C]Optcosine[/C][C]111.690085436741[/C][C]0.0280785510295003[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.2768660190620.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003






Maximum Density Values
Kernelx-valuemax. density
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.4355440772940.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 108.516524272099 & 0.0281711933124125 \tabularnewline
Epanechnikov & 111.848763494973 & 0.0281369548052213 \tabularnewline
Rectangular & 113.435544077294 & 0.0293680307075646 \tabularnewline
Triangular & 108.992558446795 & 0.0282913033948106 \tabularnewline
Biweight & 111.055373203812 & 0.0279034049660726 \tabularnewline
Cosine & 110.261982912652 & 0.0278774004500197 \tabularnewline
Optcosine & 111.690085436741 & 0.0280785510295003 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&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]108.516524272099[/C][C]0.0281711933124125[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]111.848763494973[/C][C]0.0281369548052213[/C][/ROW]
[ROW][C]Rectangular[/C][C]113.435544077294[/C][C]0.0293680307075646[/C][/ROW]
[ROW][C]Triangular[/C][C]108.992558446795[/C][C]0.0282913033948106[/C][/ROW]
[ROW][C]Biweight[/C][C]111.055373203812[/C][C]0.0279034049660726[/C][/ROW]
[ROW][C]Cosine[/C][C]110.261982912652[/C][C]0.0278774004500197[/C][/ROW]
[ROW][C]Optcosine[/C][C]111.690085436741[/C][C]0.0280785510295003[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.4355440772940.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003






Maximum Density Values
Kernelx-valuemax. density
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.5942221355260.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 108.516524272099 & 0.0281711933124125 \tabularnewline
Epanechnikov & 111.848763494973 & 0.0281369548052213 \tabularnewline
Rectangular & 113.594222135526 & 0.0293680307075646 \tabularnewline
Triangular & 108.992558446795 & 0.0282913033948106 \tabularnewline
Biweight & 111.055373203812 & 0.0279034049660726 \tabularnewline
Cosine & 110.261982912652 & 0.0278774004500197 \tabularnewline
Optcosine & 111.690085436741 & 0.0280785510295003 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&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]108.516524272099[/C][C]0.0281711933124125[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]111.848763494973[/C][C]0.0281369548052213[/C][/ROW]
[ROW][C]Rectangular[/C][C]113.594222135526[/C][C]0.0293680307075646[/C][/ROW]
[ROW][C]Triangular[/C][C]108.992558446795[/C][C]0.0282913033948106[/C][/ROW]
[ROW][C]Biweight[/C][C]111.055373203812[/C][C]0.0279034049660726[/C][/ROW]
[ROW][C]Cosine[/C][C]110.261982912652[/C][C]0.0278774004500197[/C][/ROW]
[ROW][C]Optcosine[/C][C]111.690085436741[/C][C]0.0280785510295003[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.5942221355260.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003






Maximum Density Values
Kernelx-valuemax. density
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.7529001937580.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 108.516524272099 & 0.0281711933124125 \tabularnewline
Epanechnikov & 111.848763494973 & 0.0281369548052213 \tabularnewline
Rectangular & 113.752900193758 & 0.0293680307075646 \tabularnewline
Triangular & 108.992558446795 & 0.0282913033948106 \tabularnewline
Biweight & 111.055373203812 & 0.0279034049660726 \tabularnewline
Cosine & 110.261982912652 & 0.0278774004500197 \tabularnewline
Optcosine & 111.690085436741 & 0.0280785510295003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276474&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]108.516524272099[/C][C]0.0281711933124125[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]111.848763494973[/C][C]0.0281369548052213[/C][/ROW]
[ROW][C]Rectangular[/C][C]113.752900193758[/C][C]0.0293680307075646[/C][/ROW]
[ROW][C]Triangular[/C][C]108.992558446795[/C][C]0.0282913033948106[/C][/ROW]
[ROW][C]Biweight[/C][C]111.055373203812[/C][C]0.0279034049660726[/C][/ROW]
[ROW][C]Cosine[/C][C]110.261982912652[/C][C]0.0278774004500197[/C][/ROW]
[ROW][C]Optcosine[/C][C]111.690085436741[/C][C]0.0280785510295003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276474&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276474&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
Gaussian108.5165242720990.0281711933124125
Epanechnikov111.8487634949730.0281369548052213
Rectangular113.7529001937580.0293680307075646
Triangular108.9925584467950.0282913033948106
Biweight111.0553732038120.0279034049660726
Cosine110.2619829126520.0278774004500197
Optcosine111.6900854367410.0280785510295003


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):
par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}