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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 computationThu, 27 Sep 2012 11:15:14 -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/2012/Sep/27/t1348758967hl1006rmgo1w74v.htm/, Retrieved Mon, 29 Apr 2024 15:09:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=170088, Retrieved Mon, 29 Apr 2024 15:09:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [Dichtheidsgrafiek...] [2012-09-27 15:15:14] [d241ff6d22df5f98716704005cba5463] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7,72
7,67
7,84
7,79
7,83
7,94
8,02
8,06
8,12
8,13
7,97
8,01
8
7,9
7,99
8,02
8,08
8,02
8,07
8,11
8,19
8,16
8,08
8,22
8,15
8,19
8,31
8,3
8,34
8,31
8,38
8,34
8,44
8,64
8,6
8,61
8,54
8,69
8,73
8,91
9,01
9,08
8,94
9,03
9,02
8,96
9,03
8,94
8,95
8,95
8,99
8,93
8,98
8,95
9,02
8,92
9,1
9,06
8,97
8,89
8,99
8,79
8,83
8,61
8,71
8,91
8,91
8,89
8,98
9
8,99
8,88

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'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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170088&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170088&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170088&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'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth0.168850119544991
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.168850119544991 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170088&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.168850119544991[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170088&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170088&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
Bandwidth0.168850119544991
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.812901201948450.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.94198871538542 & 1.0002925902379 \tabularnewline
Epanechnikov & 8.89417852522358 & 0.917100139751732 \tabularnewline
Rectangular & 8.81290120194845 & 0.926062109561368 \tabularnewline
Triangular & 8.94198871538542 & 0.974200968321305 \tabularnewline
Biweight & 8.9180836203045 & 0.937717784050646 \tabularnewline
Cosine & 8.92286463932068 & 0.946765540291043 \tabularnewline
Optcosine & 8.90374056325595 & 0.923105553619408 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170088&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]8.94198871538542[/C][C]1.0002925902379[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.89417852522358[/C][C]0.917100139751732[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.81290120194845[/C][C]0.926062109561368[/C][/ROW]
[ROW][C]Triangular[/C][C]8.94198871538542[/C][C]0.974200968321305[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9180836203045[/C][C]0.937717784050646[/C][/ROW]
[ROW][C]Cosine[/C][C]8.92286463932068[/C][C]0.946765540291043[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.90374056325595[/C][C]0.923105553619408[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170088&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170088&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
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.812901201948450.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.817682220964640.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.94198871538542 & 1.0002925902379 \tabularnewline
Epanechnikov & 8.89417852522358 & 0.917100139751732 \tabularnewline
Rectangular & 8.81768222096464 & 0.926062109561368 \tabularnewline
Triangular & 8.94198871538542 & 0.974200968321305 \tabularnewline
Biweight & 8.9180836203045 & 0.937717784050646 \tabularnewline
Cosine & 8.92286463932068 & 0.946765540291043 \tabularnewline
Optcosine & 8.90374056325595 & 0.923105553619408 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170088&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]8.94198871538542[/C][C]1.0002925902379[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.89417852522358[/C][C]0.917100139751732[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.81768222096464[/C][C]0.926062109561368[/C][/ROW]
[ROW][C]Triangular[/C][C]8.94198871538542[/C][C]0.974200968321305[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9180836203045[/C][C]0.937717784050646[/C][/ROW]
[ROW][C]Cosine[/C][C]8.92286463932068[/C][C]0.946765540291043[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.90374056325595[/C][C]0.923105553619408[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170088&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170088&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
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.817682220964640.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.822463239980820.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.94198871538542 & 1.0002925902379 \tabularnewline
Epanechnikov & 8.89417852522358 & 0.917100139751732 \tabularnewline
Rectangular & 8.82246323998082 & 0.926062109561368 \tabularnewline
Triangular & 8.94198871538542 & 0.974200968321305 \tabularnewline
Biweight & 8.9180836203045 & 0.937717784050646 \tabularnewline
Cosine & 8.92286463932068 & 0.946765540291043 \tabularnewline
Optcosine & 8.90374056325595 & 0.923105553619408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170088&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]8.94198871538542[/C][C]1.0002925902379[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.89417852522358[/C][C]0.917100139751732[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.82246323998082[/C][C]0.926062109561368[/C][/ROW]
[ROW][C]Triangular[/C][C]8.94198871538542[/C][C]0.974200968321305[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9180836203045[/C][C]0.937717784050646[/C][/ROW]
[ROW][C]Cosine[/C][C]8.92286463932068[/C][C]0.946765540291043[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.90374056325595[/C][C]0.923105553619408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170088&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170088&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
Gaussian8.941988715385421.0002925902379
Epanechnikov8.894178525223580.917100139751732
Rectangular8.822463239980820.926062109561368
Triangular8.941988715385420.974200968321305
Biweight8.91808362030450.937717784050646
Cosine8.922864639320680.946765540291043
Optcosine8.903740563255950.923105553619408


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')
}