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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 computationThu, 26 Sep 2013 15:22:05 -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/26/t13802234150hpqxdmyupedo0b.htm/, Retrieved Mon, 29 Apr 2024 13:23:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212186, Retrieved Mon, 29 Apr 2024 13:23:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2013-09-22 10:26:44] [5f6e4e3c532fdc05573d2888a43e29ba]
- RMPD    [Kernel Density Estimation] [] [2013-09-26 19:22:05] [2358c8bdbef440d7990b31f18da12314] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.1
20.1
20.1
20.3
20.7
20.6
20.3
19.9
19.7
19.4
19.1
18.8
18.9
18.7
18.8
19.5
19.3
19.1
19.1
19
18.8
19.2
18.9
18.7
18.5
18.4
18.3
18.3
18.3
18.5
19.2
19.4
19.1
19.5
18.8
19.3
20.4
20.9
21.1
20.6
20.4
20.8
21.1
21.6
22
22.2
22.4
22.8
22.7
22.8
22.9
22.9
22.6
21.9
20.8
20.3
20.4
21.2
21.4
20.9
20
19.5
19.2
19.3
19.4
19.5
20
20.1
19.5
18.6
18.4
18.4
19.3
19.8
19.8
19.8
20.1
20.3
19.7
20.2
20.6
21
21.4
21.9

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212186&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212186&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'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth0.4640838472622
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.4640838472622 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212186&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.4640838472622[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212186&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
Bandwidth0.4640838472622
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.3499813762640.317534065599564
Epanechnikov19.49449219981730.316483157414833
Rectangular19.59564977630460.340334828138502
Triangular19.36443245861940.320254167288838
Biweight19.42223678804070.315961089683206
Cosine19.40778570568530.316305955087099
Optcosine19.4366878703960.315894325762147

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.349981376264 & 0.317534065599564 \tabularnewline
Epanechnikov & 19.4944921998173 & 0.316483157414833 \tabularnewline
Rectangular & 19.5956497763046 & 0.340334828138502 \tabularnewline
Triangular & 19.3644324586194 & 0.320254167288838 \tabularnewline
Biweight & 19.4222367880407 & 0.315961089683206 \tabularnewline
Cosine & 19.4077857056853 & 0.316305955087099 \tabularnewline
Optcosine & 19.436687870396 & 0.315894325762147 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212186&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]19.349981376264[/C][C]0.317534065599564[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.4944921998173[/C][C]0.316483157414833[/C][/ROW]
[ROW][C]Rectangular[/C][C]19.5956497763046[/C][C]0.340334828138502[/C][/ROW]
[ROW][C]Triangular[/C][C]19.3644324586194[/C][C]0.320254167288838[/C][/ROW]
[ROW][C]Biweight[/C][C]19.4222367880407[/C][C]0.315961089683206[/C][/ROW]
[ROW][C]Cosine[/C][C]19.4077857056853[/C][C]0.316305955087099[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.436687870396[/C][C]0.315894325762147[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212186&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
Gaussian19.3499813762640.317534065599564
Epanechnikov19.49449219981730.316483157414833
Rectangular19.59564977630460.340334828138502
Triangular19.36443245861940.320254167288838
Biweight19.42223678804070.315961089683206
Cosine19.40778570568530.316305955087099
Optcosine19.4366878703960.315894325762147






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.3499813762640.317534065599564
Epanechnikov19.49449219981730.316483157414833
Rectangular19.59564977630460.340334828138502
Triangular19.37888354097470.320254167288838
Biweight19.42223678804070.315961089683206
Cosine19.40778570568530.316305955087099
Optcosine19.4366878703960.315894325762147

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.349981376264 & 0.317534065599564 \tabularnewline
Epanechnikov & 19.4944921998173 & 0.316483157414833 \tabularnewline
Rectangular & 19.5956497763046 & 0.340334828138502 \tabularnewline
Triangular & 19.3788835409747 & 0.320254167288838 \tabularnewline
Biweight & 19.4222367880407 & 0.315961089683206 \tabularnewline
Cosine & 19.4077857056853 & 0.316305955087099 \tabularnewline
Optcosine & 19.436687870396 & 0.315894325762147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212186&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]19.349981376264[/C][C]0.317534065599564[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.4944921998173[/C][C]0.316483157414833[/C][/ROW]
[ROW][C]Rectangular[/C][C]19.5956497763046[/C][C]0.340334828138502[/C][/ROW]
[ROW][C]Triangular[/C][C]19.3788835409747[/C][C]0.320254167288838[/C][/ROW]
[ROW][C]Biweight[/C][C]19.4222367880407[/C][C]0.315961089683206[/C][/ROW]
[ROW][C]Cosine[/C][C]19.4077857056853[/C][C]0.316305955087099[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.436687870396[/C][C]0.315894325762147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212186&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212186&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
Gaussian19.3499813762640.317534065599564
Epanechnikov19.49449219981730.316483157414833
Rectangular19.59564977630460.340334828138502
Triangular19.37888354097470.320254167288838
Biweight19.42223678804070.315961089683206
Cosine19.40778570568530.316305955087099
Optcosine19.4366878703960.315894325762147


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')
}