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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, 27 Sep 2014 12:14:53 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Sep/27/t1411816523f7y4t1n0jfyrj92.htm/, Retrieved Thu, 09 May 2024 21:26:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=236490, Retrieved Thu, 09 May 2024 21:26:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2014-09-24 07:35:34] [6b016f6c1fe1a99f5a52e1df91826c79]
- RMPD    [Kernel Density Estimation] [] [2014-09-27 11:14:53] [5cf6a598f846f655ef95f65053f7ffc6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
70.38
70.38
70.29
70.42
70.29
70.59
70.64
70.64
70.68
70.78
70.9
71.04
71.15
71.15
71.15
71.07
71.17
71.24
71.23
71.23
71.23
71.24
71.28
71.52
71.52
71.52
71.6
71.61
71.78
71.66
71.86
71.86
71.82
71.8
72.22
72.51
72.56
72.56
72.78
72.88
73.05
73.02
73.08
73.08
73.24
73.82
74
74.37
74.38
74.38
74.36
74.42
74.59
75.07
75.19
75.19
75.21
75.18
75.86
75.93
76.01
73.23
73.23
73.2
73.24
73.36
73.4
73.49
73.49
73.57
73.82
74.08
74.08

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236490&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236490&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth0.607963199441283
#Observations73

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.607963199441283 \tabularnewline
#Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236490&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.607963199441283[/C][/ROW]
[ROW][C]#Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236490&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
Bandwidth0.607963199441283
#Observations73






Maximum Density Values
Kernelx-valuemax. density
Gaussian71.25261223707820.239894515926856
Epanechnikov71.27094448599530.229070386068228
Rectangular71.23427998816110.227655039937882
Triangular71.23427998816110.236919276044369
Biweight71.23427998816110.232104599666635
Cosine71.23427998816110.233171582488242
Optcosine71.27094448599530.230078813246763

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 71.2526122370782 & 0.239894515926856 \tabularnewline
Epanechnikov & 71.2709444859953 & 0.229070386068228 \tabularnewline
Rectangular & 71.2342799881611 & 0.227655039937882 \tabularnewline
Triangular & 71.2342799881611 & 0.236919276044369 \tabularnewline
Biweight & 71.2342799881611 & 0.232104599666635 \tabularnewline
Cosine & 71.2342799881611 & 0.233171582488242 \tabularnewline
Optcosine & 71.2709444859953 & 0.230078813246763 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236490&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]71.2526122370782[/C][C]0.239894515926856[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]71.2709444859953[/C][C]0.229070386068228[/C][/ROW]
[ROW][C]Rectangular[/C][C]71.2342799881611[/C][C]0.227655039937882[/C][/ROW]
[ROW][C]Triangular[/C][C]71.2342799881611[/C][C]0.236919276044369[/C][/ROW]
[ROW][C]Biweight[/C][C]71.2342799881611[/C][C]0.232104599666635[/C][/ROW]
[ROW][C]Cosine[/C][C]71.2342799881611[/C][C]0.233171582488242[/C][/ROW]
[ROW][C]Optcosine[/C][C]71.2709444859953[/C][C]0.230078813246763[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236490&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236490&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
Gaussian71.25261223707820.239894515926856
Epanechnikov71.27094448599530.229070386068228
Rectangular71.23427998816110.227655039937882
Triangular71.23427998816110.236919276044369
Biweight71.23427998816110.232104599666635
Cosine71.23427998816110.233171582488242
Optcosine71.27094448599530.230078813246763






Maximum Density Values
Kernelx-valuemax. density
Gaussian71.25261223707820.239894515926856
Epanechnikov71.27094448599530.229070386068228
Rectangular71.25261223707820.227655039937882
Triangular71.23427998816110.236919276044369
Biweight71.23427998816110.232104599666635
Cosine71.23427998816110.233171582488242
Optcosine71.27094448599530.230078813246763

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 71.2526122370782 & 0.239894515926856 \tabularnewline
Epanechnikov & 71.2709444859953 & 0.229070386068228 \tabularnewline
Rectangular & 71.2526122370782 & 0.227655039937882 \tabularnewline
Triangular & 71.2342799881611 & 0.236919276044369 \tabularnewline
Biweight & 71.2342799881611 & 0.232104599666635 \tabularnewline
Cosine & 71.2342799881611 & 0.233171582488242 \tabularnewline
Optcosine & 71.2709444859953 & 0.230078813246763 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=236490&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]71.2526122370782[/C][C]0.239894515926856[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]71.2709444859953[/C][C]0.229070386068228[/C][/ROW]
[ROW][C]Rectangular[/C][C]71.2526122370782[/C][C]0.227655039937882[/C][/ROW]
[ROW][C]Triangular[/C][C]71.2342799881611[/C][C]0.236919276044369[/C][/ROW]
[ROW][C]Biweight[/C][C]71.2342799881611[/C][C]0.232104599666635[/C][/ROW]
[ROW][C]Cosine[/C][C]71.2342799881611[/C][C]0.233171582488242[/C][/ROW]
[ROW][C]Optcosine[/C][C]71.2709444859953[/C][C]0.230078813246763[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=236490&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=236490&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
Gaussian71.25261223707820.239894515926856
Epanechnikov71.27094448599530.229070386068228
Rectangular71.25261223707820.227655039937882
Triangular71.23427998816110.236919276044369
Biweight71.23427998816110.232104599666635
Cosine71.23427998816110.233171582488242
Optcosine71.27094448599530.230078813246763


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')
}