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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 16 Oct 2014 23:33:41 +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/Oct/16/t1413498831992h2ufy5wtaj9j.htm/, Retrieved Mon, 13 May 2024 06:35:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243144, Retrieved Mon, 13 May 2024 06:35:42 +0000
QR Codes:

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

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Maximum-likelihood Fitting - Normal Distribution] [Intrinsic Motivat...] [2010-10-12 11:57:21] [b98453cac15ba1066b407e146608df68]
- RMPD  [Kernel Density Estimation] [] [2011-10-18 22:33:50] [b98453cac15ba1066b407e146608df68]
- RMPD      [Kernel Density Estimation] [fhffh] [2014-10-16 22:33:41] [89eea0159e598fd4e66a35404d75d000] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
17
17
18
21
20
28
19
22
16
18
25
17
14
11
27
20
22
22
21
23
17
24
14
17
23
24
24
8
22
23
25
21
24
15
22
21
25
16
28
23
21
21
26
22
21
18
12
25
17
24
15
13
26
16
24
21
20
14
25
25
20
22
20
26
18
22
24
17
24
20
19
20
15
23
26
22
20
24
26
21
25
13
20
22
23
28
22
20
6
21
20
18
23
20
24
22
21
18
21
23
23
15
21
24
23
21
21
20
11
22
27
25
18
20
24
10
27
21
21
18
15
24
22
14
28
18
26
17
19
22
18
24
15
18
26
11
26
21
23
23
15
22
26
16
20
18
22
16
19
20
19
23
24
25
21
21
23
27
23
18
16
16

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'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth1.3610937041899
#Observations162

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.3610937041899 \tabularnewline
#Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.3610937041899[/C][/ROW]
[ROW][C]#Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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
Bandwidth1.3610937041899
#Observations162






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.75226665190550.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.6932322835589 & 0.101636537718262 \tabularnewline
Epanechnikov & 21.7522666519055 & 0.101288807606942 \tabularnewline
Rectangular & 21.7522666519055 & 0.108663685235388 \tabularnewline
Triangular & 21.9884041252921 & 0.102143293238087 \tabularnewline
Biweight & 21.9293697569455 & 0.101257264803082 \tabularnewline
Cosine & 21.8703353885988 & 0.101156539890631 \tabularnewline
Optcosine & 22.0474384936388 & 0.101132229445352 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&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]21.6932322835589[/C][C]0.101636537718262[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.7522666519055[/C][C]0.101288807606942[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.7522666519055[/C][C]0.108663685235388[/C][/ROW]
[ROW][C]Triangular[/C][C]21.9884041252921[/C][C]0.102143293238087[/C][/ROW]
[ROW][C]Biweight[/C][C]21.9293697569455[/C][C]0.101257264803082[/C][/ROW]
[ROW][C]Cosine[/C][C]21.8703353885988[/C][C]0.101156539890631[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.0474384936388[/C][C]0.101132229445352[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.75226665190550.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.81130102025220.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.6932322835589 & 0.101636537718262 \tabularnewline
Epanechnikov & 21.7522666519055 & 0.101288807606942 \tabularnewline
Rectangular & 21.8113010202522 & 0.108663685235388 \tabularnewline
Triangular & 21.9884041252921 & 0.102143293238087 \tabularnewline
Biweight & 21.9293697569455 & 0.101257264803082 \tabularnewline
Cosine & 21.8703353885988 & 0.101156539890631 \tabularnewline
Optcosine & 22.0474384936388 & 0.101132229445352 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&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]21.6932322835589[/C][C]0.101636537718262[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.7522666519055[/C][C]0.101288807606942[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.8113010202522[/C][C]0.108663685235388[/C][/ROW]
[ROW][C]Triangular[/C][C]21.9884041252921[/C][C]0.102143293238087[/C][/ROW]
[ROW][C]Biweight[/C][C]21.9293697569455[/C][C]0.101257264803082[/C][/ROW]
[ROW][C]Cosine[/C][C]21.8703353885988[/C][C]0.101156539890631[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.0474384936388[/C][C]0.101132229445352[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.81130102025220.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.87033538859880.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.6932322835589 & 0.101636537718262 \tabularnewline
Epanechnikov & 21.7522666519055 & 0.101288807606942 \tabularnewline
Rectangular & 21.8703353885988 & 0.108663685235388 \tabularnewline
Triangular & 21.9884041252921 & 0.102143293238087 \tabularnewline
Biweight & 21.9293697569455 & 0.101257264803082 \tabularnewline
Cosine & 21.8703353885988 & 0.101156539890631 \tabularnewline
Optcosine & 22.0474384936388 & 0.101132229445352 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&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]21.6932322835589[/C][C]0.101636537718262[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.7522666519055[/C][C]0.101288807606942[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.8703353885988[/C][C]0.108663685235388[/C][/ROW]
[ROW][C]Triangular[/C][C]21.9884041252921[/C][C]0.102143293238087[/C][/ROW]
[ROW][C]Biweight[/C][C]21.9293697569455[/C][C]0.101257264803082[/C][/ROW]
[ROW][C]Cosine[/C][C]21.8703353885988[/C][C]0.101156539890631[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.0474384936388[/C][C]0.101132229445352[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.87033538859880.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.92936975694550.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.6932322835589 & 0.101636537718262 \tabularnewline
Epanechnikov & 21.7522666519055 & 0.101288807606942 \tabularnewline
Rectangular & 21.9293697569455 & 0.108663685235388 \tabularnewline
Triangular & 21.9884041252921 & 0.102143293238087 \tabularnewline
Biweight & 21.9293697569455 & 0.101257264803082 \tabularnewline
Cosine & 21.8703353885988 & 0.101156539890631 \tabularnewline
Optcosine & 22.0474384936388 & 0.101132229445352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243144&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]21.6932322835589[/C][C]0.101636537718262[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.7522666519055[/C][C]0.101288807606942[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.9293697569455[/C][C]0.108663685235388[/C][/ROW]
[ROW][C]Triangular[/C][C]21.9884041252921[/C][C]0.102143293238087[/C][/ROW]
[ROW][C]Biweight[/C][C]21.9293697569455[/C][C]0.101257264803082[/C][/ROW]
[ROW][C]Cosine[/C][C]21.8703353885988[/C][C]0.101156539890631[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.0474384936388[/C][C]0.101132229445352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243144&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243144&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
Gaussian21.69323228355890.101636537718262
Epanechnikov21.75226665190550.101288807606942
Rectangular21.92936975694550.108663685235388
Triangular21.98840412529210.102143293238087
Biweight21.92936975694550.101257264803082
Cosine21.87033538859880.101156539890631
Optcosine22.04743849363880.101132229445352


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
}