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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, 20 May 2015 11:08:58 +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/2015/May/20/t14321165583f0nb3wfwo3hufm.htm/, Retrieved Mon, 29 Apr 2024 06:42:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279150, Retrieved Mon, 29 Apr 2024 06:42:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

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] [gemiddelde wekeli...] [2015-05-20 10:08:58] [0793dda36b6d92f80d1980fc1d00d6bd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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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=279150&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=279150&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279150&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
Bandwidth7
#Observations153

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 7 \tabularnewline
#Observations & 153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279150&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]7[/C][/ROW]
[ROW][C]#Observations[/C][C]153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279150&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279150&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
Bandwidth7
#Observations153






Maximum Density Values
Kernelx-valuemax. density
Gaussian88.95694716242660.0352600667487425
Epanechnikov88.95694716242660.0323364700423394
Rectangular88.28375733855190.0315359390733829
Triangular89.96673189823870.0355230264318636
Biweight88.95694716242660.0331082201244727
Cosine88.95694716242660.0334234732705258
Optcosine88.95694716242660.0325888152987527

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 88.9569471624266 & 0.0352600667487425 \tabularnewline
Epanechnikov & 88.9569471624266 & 0.0323364700423394 \tabularnewline
Rectangular & 88.2837573385519 & 0.0315359390733829 \tabularnewline
Triangular & 89.9667318982387 & 0.0355230264318636 \tabularnewline
Biweight & 88.9569471624266 & 0.0331082201244727 \tabularnewline
Cosine & 88.9569471624266 & 0.0334234732705258 \tabularnewline
Optcosine & 88.9569471624266 & 0.0325888152987527 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279150&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]88.9569471624266[/C][C]0.0352600667487425[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]88.9569471624266[/C][C]0.0323364700423394[/C][/ROW]
[ROW][C]Rectangular[/C][C]88.2837573385519[/C][C]0.0315359390733829[/C][/ROW]
[ROW][C]Triangular[/C][C]89.9667318982387[/C][C]0.0355230264318636[/C][/ROW]
[ROW][C]Biweight[/C][C]88.9569471624266[/C][C]0.0331082201244727[/C][/ROW]
[ROW][C]Cosine[/C][C]88.9569471624266[/C][C]0.0334234732705258[/C][/ROW]
[ROW][C]Optcosine[/C][C]88.9569471624266[/C][C]0.0325888152987527[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279150&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279150&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
Gaussian88.95694716242660.0352600667487425
Epanechnikov88.95694716242660.0323364700423394
Rectangular88.28375733855190.0315359390733829
Triangular89.96673189823870.0355230264318636
Biweight88.95694716242660.0331082201244727
Cosine88.95694716242660.0334234732705258
Optcosine88.95694716242660.0325888152987527






Maximum Density Values
Kernelx-valuemax. density
Gaussian88.95694716242660.0352600667487425
Epanechnikov88.95694716242660.0323364700423394
Rectangular88.95694716242660.0315359390733829
Triangular89.96673189823870.0355230264318636
Biweight88.95694716242660.0331082201244727
Cosine88.95694716242660.0334234732705258
Optcosine88.95694716242660.0325888152987527

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 88.9569471624266 & 0.0352600667487425 \tabularnewline
Epanechnikov & 88.9569471624266 & 0.0323364700423394 \tabularnewline
Rectangular & 88.9569471624266 & 0.0315359390733829 \tabularnewline
Triangular & 89.9667318982387 & 0.0355230264318636 \tabularnewline
Biweight & 88.9569471624266 & 0.0331082201244727 \tabularnewline
Cosine & 88.9569471624266 & 0.0334234732705258 \tabularnewline
Optcosine & 88.9569471624266 & 0.0325888152987527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279150&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]88.9569471624266[/C][C]0.0352600667487425[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]88.9569471624266[/C][C]0.0323364700423394[/C][/ROW]
[ROW][C]Rectangular[/C][C]88.9569471624266[/C][C]0.0315359390733829[/C][/ROW]
[ROW][C]Triangular[/C][C]89.9667318982387[/C][C]0.0355230264318636[/C][/ROW]
[ROW][C]Biweight[/C][C]88.9569471624266[/C][C]0.0331082201244727[/C][/ROW]
[ROW][C]Cosine[/C][C]88.9569471624266[/C][C]0.0334234732705258[/C][/ROW]
[ROW][C]Optcosine[/C][C]88.9569471624266[/C][C]0.0325888152987527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279150&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279150&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
Gaussian88.95694716242660.0352600667487425
Epanechnikov88.95694716242660.0323364700423394
Rectangular88.95694716242660.0315359390733829
Triangular89.96673189823870.0355230264318636
Biweight88.95694716242660.0331082201244727
Cosine88.95694716242660.0334234732705258
Optcosine88.95694716242660.0325888152987527


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 7 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
par3 <- '512'
par2 <- 'no'
par1 <- '4'
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')
}