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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 computationSun, 21 Dec 2014 15:41:10 +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/2014/Dec/21/t1419176519a98gwixefwssjc1.htm/, Retrieved Thu, 16 May 2024 16:28:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271376, Retrieved Thu, 16 May 2024 16:28:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

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] [] [2014-12-21 15:41:10] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2745
1395
1550
1378
1318
1395
1483
1049
783
1208
857
48
2681
1249
1705
1472
1413
1651
1525
1095
900
1255
984
101
2655
1309
1844
1825
1629
1718
1595
1539
1513
1475
1184
211
3387
1546
1955
1899
2415
3439
1148
1127
1186
1009
817
236
2762
1035
1500
1519
1539
1452
1409
1288
987
1542
1248
1400
4190
2185
1097
1215
1236
1374
1548
1178
902

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=271376&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=271376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271376&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
Bandwidth128.728709668687
#Observations69

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 128.728709668687 \tabularnewline
#Observations & 69 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271376&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]128.728709668687[/C][/ROW]
[ROW][C]#Observations[/C][C]69[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271376&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
Bandwidth128.728709668687
#Observations69






Maximum Density Values
Kernelx-valuemax. density
Gaussian1450.606904242970.00105713618733799
Epanechnikov1392.903903170420.00105972572647178
Rectangular1335.200902097870.001137503952892
Triangular1402.521070015850.00105065336475494
Biweight1402.521070015850.00105254173199378
Cosine1412.138236861270.00105162106463121
Optcosine1392.903903170420.0010558493552269

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1450.60690424297 & 0.00105713618733799 \tabularnewline
Epanechnikov & 1392.90390317042 & 0.00105972572647178 \tabularnewline
Rectangular & 1335.20090209787 & 0.001137503952892 \tabularnewline
Triangular & 1402.52107001585 & 0.00105065336475494 \tabularnewline
Biweight & 1402.52107001585 & 0.00105254173199378 \tabularnewline
Cosine & 1412.13823686127 & 0.00105162106463121 \tabularnewline
Optcosine & 1392.90390317042 & 0.0010558493552269 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271376&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]1450.60690424297[/C][C]0.00105713618733799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1392.90390317042[/C][C]0.00105972572647178[/C][/ROW]
[ROW][C]Rectangular[/C][C]1335.20090209787[/C][C]0.001137503952892[/C][/ROW]
[ROW][C]Triangular[/C][C]1402.52107001585[/C][C]0.00105065336475494[/C][/ROW]
[ROW][C]Biweight[/C][C]1402.52107001585[/C][C]0.00105254173199378[/C][/ROW]
[ROW][C]Cosine[/C][C]1412.13823686127[/C][C]0.00105162106463121[/C][/ROW]
[ROW][C]Optcosine[/C][C]1392.90390317042[/C][C]0.0010558493552269[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271376&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271376&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
Gaussian1450.606904242970.00105713618733799
Epanechnikov1392.903903170420.00105972572647178
Rectangular1335.200902097870.001137503952892
Triangular1402.521070015850.00105065336475494
Biweight1402.521070015850.00105254173199378
Cosine1412.138236861270.00105162106463121
Optcosine1392.903903170420.0010558493552269






Maximum Density Values
Kernelx-valuemax. density
Gaussian1450.606904242970.00105713618733799
Epanechnikov1392.903903170420.00105972572647178
Rectangular1344.81806894330.001137503952892
Triangular1402.521070015850.00105065336475494
Biweight1402.521070015850.00105254173199378
Cosine1412.138236861270.00105162106463121
Optcosine1392.903903170420.0010558493552269

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1450.60690424297 & 0.00105713618733799 \tabularnewline
Epanechnikov & 1392.90390317042 & 0.00105972572647178 \tabularnewline
Rectangular & 1344.8180689433 & 0.001137503952892 \tabularnewline
Triangular & 1402.52107001585 & 0.00105065336475494 \tabularnewline
Biweight & 1402.52107001585 & 0.00105254173199378 \tabularnewline
Cosine & 1412.13823686127 & 0.00105162106463121 \tabularnewline
Optcosine & 1392.90390317042 & 0.0010558493552269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271376&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]1450.60690424297[/C][C]0.00105713618733799[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1392.90390317042[/C][C]0.00105972572647178[/C][/ROW]
[ROW][C]Rectangular[/C][C]1344.8180689433[/C][C]0.001137503952892[/C][/ROW]
[ROW][C]Triangular[/C][C]1402.52107001585[/C][C]0.00105065336475494[/C][/ROW]
[ROW][C]Biweight[/C][C]1402.52107001585[/C][C]0.00105254173199378[/C][/ROW]
[ROW][C]Cosine[/C][C]1412.13823686127[/C][C]0.00105162106463121[/C][/ROW]
[ROW][C]Optcosine[/C][C]1392.90390317042[/C][C]0.0010558493552269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271376&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271376&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
Gaussian1450.606904242970.00105713618733799
Epanechnikov1392.903903170420.00105972572647178
Rectangular1344.81806894330.001137503952892
Triangular1402.521070015850.00105065336475494
Biweight1402.521070015850.00105254173199378
Cosine1412.138236861270.00105162106463121
Optcosine1392.903903170420.0010558493552269


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = red ; par3 = TRUE ; par4 = Unknown ;
Parameters (R input):
par1 = 0 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}