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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, 23 Sep 2013 12:34:43 -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/23/t1379954144h8jtw8dm4aqgqnt.htm/, Retrieved Sun, 28 Apr 2024 19:23:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211804, Retrieved Sun, 28 Apr 2024 19:23:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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] [] [2013-09-16 15:22:10] [cdd835b6be22d878f15dd5e149bcbc86]
- RMP     [Kernel Density Estimation] [] [2013-09-23 16:34:43] [12e977ea58b1a83461bd6217bf886aa8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3.96
3.97
3.96
3.95
3.94
3.94
3.95
3.93
3.94
3.92
3.95
3.94
3.95
3.92
3.92
3.92
3.92
3.9
3.92
3.94
3.96
3.95
3.96
3.97
3.99
4
4.05
4.08
4.09
4.12
4.14
4.15
4.15
4.15
4.15
4.2
4.22
4.22
4.22
4.23
4.3
4.29
4.32
4.31
4.35
4.34
4.35
4.38
4.39
4.38
4.34
4.33
4.33
4.33
4.33
4.32
4.35
4.35
4.35
4.36
4.38
4.41
4.43
4.42
4.43
4.43
4.42
4.46
4.44
4.41
4.41
4.46
4.5
4.58
4.61
4.65
4.55
4.63
4.69
4.72
4.71
4.74
4.77
4.78

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211804&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211804&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211804&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth0.0933959499559878
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0933959499559878 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211804&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0933959499559878[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211804&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211804&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
Bandwidth0.0933959499559878
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.358321804399771.56580734770829
Epanechnikov4.327315673877081.4603630876045
Rectangular4.304765760769671.50864099159148
Triangular4.349865586984491.52964475920805
Biweight4.347046847846071.4885454742164
Cosine4.349865586984491.50047094037031
Optcosine4.338590630430791.46729476371362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.35832180439977 & 1.56580734770829 \tabularnewline
Epanechnikov & 4.32731567387708 & 1.4603630876045 \tabularnewline
Rectangular & 4.30476576076967 & 1.50864099159148 \tabularnewline
Triangular & 4.34986558698449 & 1.52964475920805 \tabularnewline
Biweight & 4.34704684784607 & 1.4885454742164 \tabularnewline
Cosine & 4.34986558698449 & 1.50047094037031 \tabularnewline
Optcosine & 4.33859063043079 & 1.46729476371362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211804&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]4.35832180439977[/C][C]1.56580734770829[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.32731567387708[/C][C]1.4603630876045[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.30476576076967[/C][C]1.50864099159148[/C][/ROW]
[ROW][C]Triangular[/C][C]4.34986558698449[/C][C]1.52964475920805[/C][/ROW]
[ROW][C]Biweight[/C][C]4.34704684784607[/C][C]1.4885454742164[/C][/ROW]
[ROW][C]Cosine[/C][C]4.34986558698449[/C][C]1.50047094037031[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.33859063043079[/C][C]1.46729476371362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211804&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211804&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
Gaussian4.358321804399771.56580734770829
Epanechnikov4.327315673877081.4603630876045
Rectangular4.304765760769671.50864099159148
Triangular4.349865586984491.52964475920805
Biweight4.347046847846071.4885454742164
Cosine4.349865586984491.50047094037031
Optcosine4.338590630430791.46729476371362






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.358321804399771.56580734770829
Epanechnikov4.327315673877081.4603630876045
Rectangular4.30758449990811.50864099159148
Triangular4.349865586984491.52964475920805
Biweight4.347046847846071.4885454742164
Cosine4.349865586984491.50047094037031
Optcosine4.338590630430791.46729476371362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.35832180439977 & 1.56580734770829 \tabularnewline
Epanechnikov & 4.32731567387708 & 1.4603630876045 \tabularnewline
Rectangular & 4.3075844999081 & 1.50864099159148 \tabularnewline
Triangular & 4.34986558698449 & 1.52964475920805 \tabularnewline
Biweight & 4.34704684784607 & 1.4885454742164 \tabularnewline
Cosine & 4.34986558698449 & 1.50047094037031 \tabularnewline
Optcosine & 4.33859063043079 & 1.46729476371362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211804&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]4.35832180439977[/C][C]1.56580734770829[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.32731567387708[/C][C]1.4603630876045[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.3075844999081[/C][C]1.50864099159148[/C][/ROW]
[ROW][C]Triangular[/C][C]4.34986558698449[/C][C]1.52964475920805[/C][/ROW]
[ROW][C]Biweight[/C][C]4.34704684784607[/C][C]1.4885454742164[/C][/ROW]
[ROW][C]Cosine[/C][C]4.34986558698449[/C][C]1.50047094037031[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.33859063043079[/C][C]1.46729476371362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211804&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211804&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
Gaussian4.358321804399771.56580734770829
Epanechnikov4.327315673877081.4603630876045
Rectangular4.30758449990811.50864099159148
Triangular4.349865586984491.52964475920805
Biweight4.347046847846071.4885454742164
Cosine4.349865586984491.50047094037031
Optcosine4.338590630430791.46729476371362


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')
}