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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 computationTue, 12 Feb 2013 14:30:52 -0500
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/Feb/12/t1360698364b5tfx1hs6mklj9z.htm/, Retrieved Sun, 28 Apr 2024 20:56:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206442, Retrieved Sun, 28 Apr 2024 20:56:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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] [Gemiddelde consum...] [2013-02-04 23:50:25] [812272bcf10cd97986bd11f9adf3f369]
- R PD  [Univariate Data Series] [] [2013-02-12 13:22:58] [812272bcf10cd97986bd11f9adf3f369]
- RMPD      [Kernel Density Estimation] [Maaltijd in resta...] [2013-02-12 19:30:52] [1f4ca98ed28755372cdf3133ccb2c2d2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.11	
9.06	
9.11	
9.13	
9.13	
9.19	
9.2	
9.23	
9.24	
9.28	
9.32	
9.32	
9.32	
9.36	
9.37	
9.38	
9.41	
9.44	
9.44	
9.44	
9.47	
9.48	
9.56	
9.58	
9.56	
9.58	
9.7	
9.74	
9.76	
9.78	
9.84	
9.88	
9.96	
9.97	
9.96	
9.96	
9.96	
10.02	
10.08	
10.09	
10.12	
10.14	
10.17	
10.22	
10.25	
10.25	
10.26	
10.34	
10.33	
10.3	
10.33	
10.33	
10.37	
10.44	
10.45	
10.45	
10.44	
10.43	
10.4	
10.43	
10.47	
10.52	
10.55	
10.5	
10.44	
10.47	
10.5	
10.54	
10.55	
10.53	
10.54	
10.54

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206442&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]6 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=206442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206442&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 time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth0.189494091428549
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.189494091428549 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206442&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.189494091428549[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206442&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
Bandwidth0.189494091428549
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.23425937339670.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10.3884842979703 & 0.805549192948634 \tabularnewline
Epanechnikov & 10.3113718356835 & 0.77619512585654 \tabularnewline
Rectangular & 10.2342593733967 & 0.846332851678212 \tabularnewline
Triangular & 10.3422168205982 & 0.777095457138796 \tabularnewline
Biweight & 10.3422168205982 & 0.779185646243322 \tabularnewline
Cosine & 10.3524984822365 & 0.782078989672011 \tabularnewline
Optcosine & 10.3267943281409 & 0.775871729376687 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206442&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]10.3884842979703[/C][C]0.805549192948634[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10.3113718356835[/C][C]0.77619512585654[/C][/ROW]
[ROW][C]Rectangular[/C][C]10.2342593733967[/C][C]0.846332851678212[/C][/ROW]
[ROW][C]Triangular[/C][C]10.3422168205982[/C][C]0.777095457138796[/C][/ROW]
[ROW][C]Biweight[/C][C]10.3422168205982[/C][C]0.779185646243322[/C][/ROW]
[ROW][C]Cosine[/C][C]10.3524984822365[/C][C]0.782078989672011[/C][/ROW]
[ROW][C]Optcosine[/C][C]10.3267943281409[/C][C]0.775871729376687[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206442&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
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.23425937339670.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687






Maximum Density Values
Kernelx-valuemax. density
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.25996352749230.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10.3884842979703 & 0.805549192948634 \tabularnewline
Epanechnikov & 10.3113718356835 & 0.77619512585654 \tabularnewline
Rectangular & 10.2599635274923 & 0.846332851678212 \tabularnewline
Triangular & 10.3422168205982 & 0.777095457138796 \tabularnewline
Biweight & 10.3422168205982 & 0.779185646243322 \tabularnewline
Cosine & 10.3524984822365 & 0.782078989672011 \tabularnewline
Optcosine & 10.3267943281409 & 0.775871729376687 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206442&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]10.3884842979703[/C][C]0.805549192948634[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10.3113718356835[/C][C]0.77619512585654[/C][/ROW]
[ROW][C]Rectangular[/C][C]10.2599635274923[/C][C]0.846332851678212[/C][/ROW]
[ROW][C]Triangular[/C][C]10.3422168205982[/C][C]0.777095457138796[/C][/ROW]
[ROW][C]Biweight[/C][C]10.3422168205982[/C][C]0.779185646243322[/C][/ROW]
[ROW][C]Cosine[/C][C]10.3524984822365[/C][C]0.782078989672011[/C][/ROW]
[ROW][C]Optcosine[/C][C]10.3267943281409[/C][C]0.775871729376687[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206442&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
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.25996352749230.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687






Maximum Density Values
Kernelx-valuemax. density
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.26510435831140.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 10.3884842979703 & 0.805549192948634 \tabularnewline
Epanechnikov & 10.3113718356835 & 0.77619512585654 \tabularnewline
Rectangular & 10.2651043583114 & 0.846332851678212 \tabularnewline
Triangular & 10.3422168205982 & 0.777095457138796 \tabularnewline
Biweight & 10.3422168205982 & 0.779185646243322 \tabularnewline
Cosine & 10.3524984822365 & 0.782078989672011 \tabularnewline
Optcosine & 10.3267943281409 & 0.775871729376687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206442&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]10.3884842979703[/C][C]0.805549192948634[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]10.3113718356835[/C][C]0.77619512585654[/C][/ROW]
[ROW][C]Rectangular[/C][C]10.2651043583114[/C][C]0.846332851678212[/C][/ROW]
[ROW][C]Triangular[/C][C]10.3422168205982[/C][C]0.777095457138796[/C][/ROW]
[ROW][C]Biweight[/C][C]10.3422168205982[/C][C]0.779185646243322[/C][/ROW]
[ROW][C]Cosine[/C][C]10.3524984822365[/C][C]0.782078989672011[/C][/ROW]
[ROW][C]Optcosine[/C][C]10.3267943281409[/C][C]0.775871729376687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206442&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206442&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
Gaussian10.38848429797030.805549192948634
Epanechnikov10.31137183568350.77619512585654
Rectangular10.26510435831140.846332851678212
Triangular10.34221682059820.777095457138796
Biweight10.34221682059820.779185646243322
Cosine10.35249848223650.782078989672011
Optcosine10.32679432814090.775871729376687


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 100 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')
}