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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, 28 Sep 2013 14:59:58 -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/28/t1380394843do43pydh07jb59b.htm/, Retrieved Mon, 29 Apr 2024 14:34:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212375, Retrieved Mon, 29 Apr 2024 14:34:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64

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] [] [2013-09-28 18:59:58] [790f0636b450c832b3696ec959e2e52b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
20.89
21.04
21.07
21.12
21.25
21.24
21.24
21.22
21.29
21.25
21.15
21.16
21.16
21.52
21.59
21.6
21.68
21.67
21.67
21.65
21.74
21.72
21.84
21.94
21.94
21.95
21.96
22.1
22.13
22.18
22.18
22.27
22.3
22.04
22.05
22.06
22.06
22.06
21.97
22.03
22.08
22.13
22.13
22.4
22.4
22.12
22.22
22.14
22.14
22.19
22.29
22.24
22.26
22.29
22.29
22.29
22.29
22.35
22.39
22.43
22.43
22.11
22.12
22.05
22.05
22.08
22.08
22.09
22.09
22.24
22.25
22.24
22.24
22.25
22.28
22.23
22.29
22.31
22.31
22.31
22.39
22.42
22.42
22.42

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=212375&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=212375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212375&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
Bandwidth0.148819664953487
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.148819664953487 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212375&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.148819664953487[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212375&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
Bandwidth0.148819664953487
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.19562284509511.37612408821514
Epanechnikov22.19562284509511.35659660630846
Rectangular22.18133956922591.40863866022865
Triangular22.21942830487711.34113554521862
Biweight22.19562284509511.35958464348416
Cosine22.19562284509511.36105241650093
Optcosine22.19562284509511.35620287955006

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.1956228450951 & 1.37612408821514 \tabularnewline
Epanechnikov & 22.1956228450951 & 1.35659660630846 \tabularnewline
Rectangular & 22.1813395692259 & 1.40863866022865 \tabularnewline
Triangular & 22.2194283048771 & 1.34113554521862 \tabularnewline
Biweight & 22.1956228450951 & 1.35958464348416 \tabularnewline
Cosine & 22.1956228450951 & 1.36105241650093 \tabularnewline
Optcosine & 22.1956228450951 & 1.35620287955006 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212375&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]22.1956228450951[/C][C]1.37612408821514[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.1956228450951[/C][C]1.35659660630846[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.1813395692259[/C][C]1.40863866022865[/C][/ROW]
[ROW][C]Triangular[/C][C]22.2194283048771[/C][C]1.34113554521862[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1956228450951[/C][C]1.35958464348416[/C][/ROW]
[ROW][C]Cosine[/C][C]22.1956228450951[/C][C]1.36105241650093[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.1956228450951[/C][C]1.35620287955006[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212375&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212375&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
Gaussian22.19562284509511.37612408821514
Epanechnikov22.19562284509511.35659660630846
Rectangular22.18133956922591.40863866022865
Triangular22.21942830487711.34113554521862
Biweight22.19562284509511.35958464348416
Cosine22.19562284509511.36105241650093
Optcosine22.19562284509511.35620287955006






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.19562284509511.37612408821514
Epanechnikov22.19562284509511.35659660630846
Rectangular22.18610066118231.40863866022865
Triangular22.21942830487711.34113554521862
Biweight22.19562284509511.35958464348416
Cosine22.19562284509511.36105241650093
Optcosine22.19562284509511.35620287955006

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.1956228450951 & 1.37612408821514 \tabularnewline
Epanechnikov & 22.1956228450951 & 1.35659660630846 \tabularnewline
Rectangular & 22.1861006611823 & 1.40863866022865 \tabularnewline
Triangular & 22.2194283048771 & 1.34113554521862 \tabularnewline
Biweight & 22.1956228450951 & 1.35958464348416 \tabularnewline
Cosine & 22.1956228450951 & 1.36105241650093 \tabularnewline
Optcosine & 22.1956228450951 & 1.35620287955006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212375&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]22.1956228450951[/C][C]1.37612408821514[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.1956228450951[/C][C]1.35659660630846[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.1861006611823[/C][C]1.40863866022865[/C][/ROW]
[ROW][C]Triangular[/C][C]22.2194283048771[/C][C]1.34113554521862[/C][/ROW]
[ROW][C]Biweight[/C][C]22.1956228450951[/C][C]1.35958464348416[/C][/ROW]
[ROW][C]Cosine[/C][C]22.1956228450951[/C][C]1.36105241650093[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.1956228450951[/C][C]1.35620287955006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212375&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212375&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
Gaussian22.19562284509511.37612408821514
Epanechnikov22.19562284509511.35659660630846
Rectangular22.18610066118231.40863866022865
Triangular22.21942830487711.34113554521862
Biweight22.19562284509511.35958464348416
Cosine22.19562284509511.36105241650093
Optcosine22.19562284509511.35620287955006


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')
}