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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 computationTue, 24 Sep 2013 17:26:52 -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/2013/Sep/24/t1380058083nqeiwdy63ajqwk3.htm/, Retrieved Tue, 30 Apr 2024 12:04:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211896, Retrieved Tue, 30 Apr 2024 12:04:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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] [] [2013-09-16 19:43:38] [4137616dc99e71bd0abe7ac75f4ed0c6]
- RMPD  [Histogram] [] [2013-09-24 21:13:43] [74be16979710d4c4e7c6647856088456]
- RMP       [Kernel Density Estimation] [] [2013-09-24 21:26:52] [548ba37af61861f215c3470847960b18] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
462.23
464.79
465.22
468.52
469.02
469.15
469.15
469.15
469.15
469.41
469.45
469.45
469.93
477.19
478.97
480.44
480.56
481.8
483.24
483.45
483.53
483.59
483.59
483.59
492.36
495.71
499.29
499.78
500
500
500.29
500.42
500.61
498.9
499.06
496.61
498.41
501.26
505.4
506.07
506.2
507.14
507.14
507.28
507.34
507.48
506.97
506.97
510.1
515.84
519
520.1
521.26
521.04
521.12
521.12
521.1
521.16
521.14
521.13
522.17
531.39
532.12
533.34
535.72
536.25
536.25
536.68
536.76
536.79
536.99
536.99
542.38
544.1
546.96
547.04
550.27
550.32
551.17
552.83
552.35
552.44
552.47
548.78

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211896&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211896&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211896&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth10.0140629513844
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 10.0140629513844 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211896&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]10.0140629513844[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211896&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211896&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
Bandwidth10.0140629513844
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian504.4337456635280.0126986449452908
Epanechnikov508.2672034134460.0122133909995743
Rectangular506.2030338557980.0126975957899233
Triangular500.8951692789880.0125395046324048
Biweight505.9081524904190.0122825754660374
Cosine505.3183897596630.0123450444185596
Optcosine508.2672034134460.0121767211587197

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 504.433745663528 & 0.0126986449452908 \tabularnewline
Epanechnikov & 508.267203413446 & 0.0122133909995743 \tabularnewline
Rectangular & 506.203033855798 & 0.0126975957899233 \tabularnewline
Triangular & 500.895169278988 & 0.0125395046324048 \tabularnewline
Biweight & 505.908152490419 & 0.0122825754660374 \tabularnewline
Cosine & 505.318389759663 & 0.0123450444185596 \tabularnewline
Optcosine & 508.267203413446 & 0.0121767211587197 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211896&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]504.433745663528[/C][C]0.0126986449452908[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]508.267203413446[/C][C]0.0122133909995743[/C][/ROW]
[ROW][C]Rectangular[/C][C]506.203033855798[/C][C]0.0126975957899233[/C][/ROW]
[ROW][C]Triangular[/C][C]500.895169278988[/C][C]0.0125395046324048[/C][/ROW]
[ROW][C]Biweight[/C][C]505.908152490419[/C][C]0.0122825754660374[/C][/ROW]
[ROW][C]Cosine[/C][C]505.318389759663[/C][C]0.0123450444185596[/C][/ROW]
[ROW][C]Optcosine[/C][C]508.267203413446[/C][C]0.0121767211587197[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211896&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211896&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
Gaussian504.4337456635280.0126986449452908
Epanechnikov508.2672034134460.0122133909995743
Rectangular506.2030338557980.0126975957899233
Triangular500.8951692789880.0125395046324048
Biweight505.9081524904190.0122825754660374
Cosine505.3183897596630.0123450444185596
Optcosine508.2672034134460.0121767211587197






Maximum Density Values
Kernelx-valuemax. density
Gaussian504.4337456635280.0126986449452908
Epanechnikov508.2672034134460.0122133909995743
Rectangular506.4979152211760.0126975957899233
Triangular500.8951692789880.0125395046324048
Biweight505.9081524904190.0122825754660374
Cosine505.3183897596630.0123450444185596
Optcosine508.2672034134460.0121767211587197

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 504.433745663528 & 0.0126986449452908 \tabularnewline
Epanechnikov & 508.267203413446 & 0.0122133909995743 \tabularnewline
Rectangular & 506.497915221176 & 0.0126975957899233 \tabularnewline
Triangular & 500.895169278988 & 0.0125395046324048 \tabularnewline
Biweight & 505.908152490419 & 0.0122825754660374 \tabularnewline
Cosine & 505.318389759663 & 0.0123450444185596 \tabularnewline
Optcosine & 508.267203413446 & 0.0121767211587197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211896&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]504.433745663528[/C][C]0.0126986449452908[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]508.267203413446[/C][C]0.0122133909995743[/C][/ROW]
[ROW][C]Rectangular[/C][C]506.497915221176[/C][C]0.0126975957899233[/C][/ROW]
[ROW][C]Triangular[/C][C]500.895169278988[/C][C]0.0125395046324048[/C][/ROW]
[ROW][C]Biweight[/C][C]505.908152490419[/C][C]0.0122825754660374[/C][/ROW]
[ROW][C]Cosine[/C][C]505.318389759663[/C][C]0.0123450444185596[/C][/ROW]
[ROW][C]Optcosine[/C][C]508.267203413446[/C][C]0.0121767211587197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211896&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211896&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
Gaussian504.4337456635280.0126986449452908
Epanechnikov508.2672034134460.0122133909995743
Rectangular506.4979152211760.0126975957899233
Triangular500.8951692789880.0125395046324048
Biweight505.9081524904190.0122825754660374
Cosine505.3183897596630.0123450444185596
Optcosine508.2672034134460.0121767211587197


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')
}