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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationMon, 12 Nov 2012 11:05:28 -0500
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/Nov/12/t13527363995s24k3dtntv1ffs.htm/, Retrieved Sun, 28 Apr 2024 19:33:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=188083, Retrieved Sun, 28 Apr 2024 19:33:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

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] [kernel] [2012-11-12 16:05:28] [081b45eff66f9ee50ac0b17603ac2bbc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18.22603393
-10.43820584
-10.62325608
-24.9074432
7.106998638
55.0334049
0.932005188
-29.67536499
-9.653445224
-17.28049436
1.559134115
-16.62295294
52.2417288
2.139074683
29.97394343
-4.257249568
-22.98148029
-39.09036598
-5.185391
7.708022367
0.105725675
16.67964537
-14.11309067
26.96725579
2.886037717
3.751564011
-5.320386827
4.599299868
-14.76571782
-3.909481256
-2.164384006
-1.330984011
-8.368294079
-3.507429943
2.653445127
22.19946426
-29.87441448
22.37994334
-11.63650931
0.002101329
-4.518992416
-6.325030147
22.88279281
17.93361465
15.40539308
6.180331784
2.088614755
-24.93747351
-29.66679297
-17.29405038
0.474548418
10.08374153
24.78323026
7.859558974
-16.71691829
3.869912015
2.502698929
-2.049714186
7.864550303
-7.547517662
-13.66281683
-0.415195524
-2.77171802
14.54200091
10.40434879
-13.57347601
0.21255987
1.441069462

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188083&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]10 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=188083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188083&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 time10 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth5.26540193632531
#Observations68

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 5.26540193632531 \tabularnewline
#Observations & 68 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188083&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]5.26540193632531[/C][/ROW]
[ROW][C]#Observations[/C][C]68[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188083&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
Bandwidth5.26540193632531
#Observations68






Maximum Density Values
Kernelx-valuemax. density
Gaussian-0.02412815484038160.0295794191522233
Epanechnikov-0.2701480814508550.0285511673105923
Rectangular-0.7621879346718010.0280766358401888
Triangular0.2218917717700920.0291497171745017
Biweight-0.2701480814508550.0287823236291367
Cosine-0.2701480814508550.0288909077366081
Optcosine-0.2701480814508550.028644006675019

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & -0.0241281548403816 & 0.0295794191522233 \tabularnewline
Epanechnikov & -0.270148081450855 & 0.0285511673105923 \tabularnewline
Rectangular & -0.762187934671801 & 0.0280766358401888 \tabularnewline
Triangular & 0.221891771770092 & 0.0291497171745017 \tabularnewline
Biweight & -0.270148081450855 & 0.0287823236291367 \tabularnewline
Cosine & -0.270148081450855 & 0.0288909077366081 \tabularnewline
Optcosine & -0.270148081450855 & 0.028644006675019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=188083&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]-0.0241281548403816[/C][C]0.0295794191522233[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]-0.270148081450855[/C][C]0.0285511673105923[/C][/ROW]
[ROW][C]Rectangular[/C][C]-0.762187934671801[/C][C]0.0280766358401888[/C][/ROW]
[ROW][C]Triangular[/C][C]0.221891771770092[/C][C]0.0291497171745017[/C][/ROW]
[ROW][C]Biweight[/C][C]-0.270148081450855[/C][C]0.0287823236291367[/C][/ROW]
[ROW][C]Cosine[/C][C]-0.270148081450855[/C][C]0.0288909077366081[/C][/ROW]
[ROW][C]Optcosine[/C][C]-0.270148081450855[/C][C]0.028644006675019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=188083&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=188083&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
Gaussian-0.02412815484038160.0295794191522233
Epanechnikov-0.2701480814508550.0285511673105923
Rectangular-0.7621879346718010.0280766358401888
Triangular0.2218917717700920.0291497171745017
Biweight-0.2701480814508550.0287823236291367
Cosine-0.2701480814508550.0288909077366081
Optcosine-0.2701480814508550.028644006675019


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')
}