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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 computationWed, 04 Feb 2015 14:28:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Feb/04/t1423060157vkth5ziz1fyvvir.htm/, Retrieved Sat, 18 May 2024 07:03:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=276607, Retrieved Sat, 18 May 2024 07:03:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

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] [Gauss-curve inflatie] [2015-02-04 14:28:26] [d7b65c9a7c286d706dc95a87d306e880] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
2,2
2,2
2
2,3
2,6
3,2
3,2
3,1
2,8
2,3
1,9
1,9
2
2
1,8
1,6
1,4
0,2
0,3
0,4
0,7
1
1,1
0,8
0,8
1
1,1
1
0,8
1,6
1,5
1,6
1,6
1,6
1,9
2
1,9
2
2,1
2,3
2,3
2,6
2,6
2,7
2,6
2,6
2,4
2,5
2,5
2,5
2,4
2,1
2,1
2,3
2,3
2,3
2,9
2,8
2,9
3
3
2,9
2,6
2,8
2,9
3,1
2,8
2,4
1,6
1,5
1,7

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=276607&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=276607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Bandwidth0.283072354883125
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.283072354883125 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276607&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.283072354883125[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Bandwidth0.283072354883125
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.366607581945520.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.31144005792244 & 0.531015987458524 \tabularnewline
Epanechnikov & 2.39419134395706 & 0.533153656756562 \tabularnewline
Rectangular & 2.36660758194552 & 0.552387738357863 \tabularnewline
Triangular & 2.31144005792244 & 0.531325527547831 \tabularnewline
Biweight & 2.36660758194552 & 0.529199146551343 \tabularnewline
Cosine & 2.33902381993398 & 0.528842513515528 \tabularnewline
Optcosine & 2.38499675661988 & 0.531977863380611 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276607&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]2.31144005792244[/C][C]0.531015987458524[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.39419134395706[/C][C]0.533153656756562[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.36660758194552[/C][C]0.552387738357863[/C][/ROW]
[ROW][C]Triangular[/C][C]2.31144005792244[/C][C]0.531325527547831[/C][/ROW]
[ROW][C]Biweight[/C][C]2.36660758194552[/C][C]0.529199146551343[/C][/ROW]
[ROW][C]Cosine[/C][C]2.33902381993398[/C][C]0.528842513515528[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.38499675661988[/C][C]0.531977863380611[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276607&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.366607581945520.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.37580216928270.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.31144005792244 & 0.531015987458524 \tabularnewline
Epanechnikov & 2.39419134395706 & 0.533153656756562 \tabularnewline
Rectangular & 2.3758021692827 & 0.552387738357863 \tabularnewline
Triangular & 2.31144005792244 & 0.531325527547831 \tabularnewline
Biweight & 2.36660758194552 & 0.529199146551343 \tabularnewline
Cosine & 2.33902381993398 & 0.528842513515528 \tabularnewline
Optcosine & 2.38499675661988 & 0.531977863380611 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276607&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]2.31144005792244[/C][C]0.531015987458524[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.39419134395706[/C][C]0.533153656756562[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.3758021692827[/C][C]0.552387738357863[/C][/ROW]
[ROW][C]Triangular[/C][C]2.31144005792244[/C][C]0.531325527547831[/C][/ROW]
[ROW][C]Biweight[/C][C]2.36660758194552[/C][C]0.529199146551343[/C][/ROW]
[ROW][C]Cosine[/C][C]2.33902381993398[/C][C]0.528842513515528[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.38499675661988[/C][C]0.531977863380611[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276607&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.37580216928270.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.384996756619880.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.31144005792244 & 0.531015987458524 \tabularnewline
Epanechnikov & 2.39419134395706 & 0.533153656756562 \tabularnewline
Rectangular & 2.38499675661988 & 0.552387738357863 \tabularnewline
Triangular & 2.31144005792244 & 0.531325527547831 \tabularnewline
Biweight & 2.36660758194552 & 0.529199146551343 \tabularnewline
Cosine & 2.33902381993398 & 0.528842513515528 \tabularnewline
Optcosine & 2.38499675661988 & 0.531977863380611 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276607&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]2.31144005792244[/C][C]0.531015987458524[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.39419134395706[/C][C]0.533153656756562[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.38499675661988[/C][C]0.552387738357863[/C][/ROW]
[ROW][C]Triangular[/C][C]2.31144005792244[/C][C]0.531325527547831[/C][/ROW]
[ROW][C]Biweight[/C][C]2.36660758194552[/C][C]0.529199146551343[/C][/ROW]
[ROW][C]Cosine[/C][C]2.33902381993398[/C][C]0.528842513515528[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.38499675661988[/C][C]0.531977863380611[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276607&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.384996756619880.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611






Maximum Density Values
Kernelx-valuemax. density
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.476942629991670.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.31144005792244 & 0.531015987458524 \tabularnewline
Epanechnikov & 2.39419134395706 & 0.533153656756562 \tabularnewline
Rectangular & 2.47694262999167 & 0.552387738357863 \tabularnewline
Triangular & 2.31144005792244 & 0.531325527547831 \tabularnewline
Biweight & 2.36660758194552 & 0.529199146551343 \tabularnewline
Cosine & 2.33902381993398 & 0.528842513515528 \tabularnewline
Optcosine & 2.38499675661988 & 0.531977863380611 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276607&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]2.31144005792244[/C][C]0.531015987458524[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.39419134395706[/C][C]0.533153656756562[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.47694262999167[/C][C]0.552387738357863[/C][/ROW]
[ROW][C]Triangular[/C][C]2.31144005792244[/C][C]0.531325527547831[/C][/ROW]
[ROW][C]Biweight[/C][C]2.36660758194552[/C][C]0.529199146551343[/C][/ROW]
[ROW][C]Cosine[/C][C]2.33902381993398[/C][C]0.528842513515528[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.38499675661988[/C][C]0.531977863380611[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276607&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276607&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
Gaussian2.311440057922440.531015987458524
Epanechnikov2.394191343957060.533153656756562
Rectangular2.476942629991670.552387738357863
Triangular2.311440057922440.531325527547831
Biweight2.366607581945520.529199146551343
Cosine2.339023819933980.528842513515528
Optcosine2.384996756619880.531977863380611


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')
}