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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, 27 Sep 2014 10:06:06 +0100
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/Sep/27/t14118088208x391jmsn4tlur0.htm/, Retrieved Thu, 09 May 2024 22:33:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=236453, Retrieved Thu, 09 May 2024 22:33:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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] [] [2014-09-23 12:59:10] [4df2cd86c9043e1a56e9383f8c504201]
- RMP     [Kernel Density Estimation] [] [2014-09-27 09:06:06] [062c419fa600f620f2df94d64c8876ba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
53
47
49
44
48
51
47
44
33
47
41
36
46
24
17
22
30
24
18
24
24
28
19
22
26
14
16
21
15
23
29
17
24
18
22
8
26
22
34
25
20
35
38
24
14
25
31
17
32
27
30
19
36
27
28
38
26
25
30
27
30
50
48
34
41
26
39
33
38
28
36
20
39
22
32
32
31
28
44
40
32
35
32
31
41
23
36
36
42
36
64
30
25
51
38
27

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth3.77408346200705
#Observations96

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 3.77408346200705 \tabularnewline
#Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]3.77408346200705[/C][/ROW]
[ROW][C]#Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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
Bandwidth3.77408346200705
#Observations96






Maximum Density Values
Kernelx-valuemax. density
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular29.76692312863460.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 26.6888604761085 & 0.0371994068775799 \tabularnewline
Epanechnikov & 28.2278918023716 & 0.0369766427708446 \tabularnewline
Rectangular & 29.7669231286346 & 0.0382444025815603 \tabularnewline
Triangular & 26.9966667413611 & 0.0368236932835074 \tabularnewline
Biweight & 27.45837613924 & 0.0369857478497302 \tabularnewline
Cosine & 27.3044730066137 & 0.0370014233199682 \tabularnewline
Optcosine & 28.2278918023716 & 0.0369688090963879 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&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]26.6888604761085[/C][C]0.0371994068775799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]28.2278918023716[/C][C]0.0369766427708446[/C][/ROW]
[ROW][C]Rectangular[/C][C]29.7669231286346[/C][C]0.0382444025815603[/C][/ROW]
[ROW][C]Triangular[/C][C]26.9966667413611[/C][C]0.0368236932835074[/C][/ROW]
[ROW][C]Biweight[/C][C]27.45837613924[/C][C]0.0369857478497302[/C][/ROW]
[ROW][C]Cosine[/C][C]27.3044730066137[/C][C]0.0370014233199682[/C][/ROW]
[ROW][C]Optcosine[/C][C]28.2278918023716[/C][C]0.0369688090963879[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular29.76692312863460.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879






Maximum Density Values
Kernelx-valuemax. density
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular29.92082626126090.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 26.6888604761085 & 0.0371994068775799 \tabularnewline
Epanechnikov & 28.2278918023716 & 0.0369766427708446 \tabularnewline
Rectangular & 29.9208262612609 & 0.0382444025815603 \tabularnewline
Triangular & 26.9966667413611 & 0.0368236932835074 \tabularnewline
Biweight & 27.45837613924 & 0.0369857478497302 \tabularnewline
Cosine & 27.3044730066137 & 0.0370014233199682 \tabularnewline
Optcosine & 28.2278918023716 & 0.0369688090963879 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&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]26.6888604761085[/C][C]0.0371994068775799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]28.2278918023716[/C][C]0.0369766427708446[/C][/ROW]
[ROW][C]Rectangular[/C][C]29.9208262612609[/C][C]0.0382444025815603[/C][/ROW]
[ROW][C]Triangular[/C][C]26.9966667413611[/C][C]0.0368236932835074[/C][/ROW]
[ROW][C]Biweight[/C][C]27.45837613924[/C][C]0.0369857478497302[/C][/ROW]
[ROW][C]Cosine[/C][C]27.3044730066137[/C][C]0.0370014233199682[/C][/ROW]
[ROW][C]Optcosine[/C][C]28.2278918023716[/C][C]0.0369688090963879[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular29.92082626126090.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879






Maximum Density Values
Kernelx-valuemax. density
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular30.07472939388720.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 26.6888604761085 & 0.0371994068775799 \tabularnewline
Epanechnikov & 28.2278918023716 & 0.0369766427708446 \tabularnewline
Rectangular & 30.0747293938872 & 0.0382444025815603 \tabularnewline
Triangular & 26.9966667413611 & 0.0368236932835074 \tabularnewline
Biweight & 27.45837613924 & 0.0369857478497302 \tabularnewline
Cosine & 27.3044730066137 & 0.0370014233199682 \tabularnewline
Optcosine & 28.2278918023716 & 0.0369688090963879 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&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]26.6888604761085[/C][C]0.0371994068775799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]28.2278918023716[/C][C]0.0369766427708446[/C][/ROW]
[ROW][C]Rectangular[/C][C]30.0747293938872[/C][C]0.0382444025815603[/C][/ROW]
[ROW][C]Triangular[/C][C]26.9966667413611[/C][C]0.0368236932835074[/C][/ROW]
[ROW][C]Biweight[/C][C]27.45837613924[/C][C]0.0369857478497302[/C][/ROW]
[ROW][C]Cosine[/C][C]27.3044730066137[/C][C]0.0370014233199682[/C][/ROW]
[ROW][C]Optcosine[/C][C]28.2278918023716[/C][C]0.0369688090963879[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular30.07472939388720.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879






Maximum Density Values
Kernelx-valuemax. density
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular30.22863252651350.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 26.6888604761085 & 0.0371994068775799 \tabularnewline
Epanechnikov & 28.2278918023716 & 0.0369766427708446 \tabularnewline
Rectangular & 30.2286325265135 & 0.0382444025815603 \tabularnewline
Triangular & 26.9966667413611 & 0.0368236932835074 \tabularnewline
Biweight & 27.45837613924 & 0.0369857478497302 \tabularnewline
Cosine & 27.3044730066137 & 0.0370014233199682 \tabularnewline
Optcosine & 28.2278918023716 & 0.0369688090963879 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236453&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]26.6888604761085[/C][C]0.0371994068775799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]28.2278918023716[/C][C]0.0369766427708446[/C][/ROW]
[ROW][C]Rectangular[/C][C]30.2286325265135[/C][C]0.0382444025815603[/C][/ROW]
[ROW][C]Triangular[/C][C]26.9966667413611[/C][C]0.0368236932835074[/C][/ROW]
[ROW][C]Biweight[/C][C]27.45837613924[/C][C]0.0369857478497302[/C][/ROW]
[ROW][C]Cosine[/C][C]27.3044730066137[/C][C]0.0370014233199682[/C][/ROW]
[ROW][C]Optcosine[/C][C]28.2278918023716[/C][C]0.0369688090963879[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236453&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236453&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
Gaussian26.68886047610850.0371994068775799
Epanechnikov28.22789180237160.0369766427708446
Rectangular30.22863252651350.0382444025815603
Triangular26.99666674136110.0368236932835074
Biweight27.458376139240.0369857478497302
Cosine27.30447300661370.0370014233199682
Optcosine28.22789180237160.0369688090963879


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')
}