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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 computationTue, 16 Oct 2012 08:10:16 -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/Oct/16/t1350389431pcmtu1ixjf59dr7.htm/, Retrieved Tue, 30 Apr 2024 09:43:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=178631, Retrieved Tue, 30 Apr 2024 09:43:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

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] [Question4] [2012-10-16 11:24:46] [3ba5358ad212dca7c498c7fc6d6ebde5]
- RMPD  [Notched Boxplots] [] [2012-10-16 11:34:25] [3ba5358ad212dca7c498c7fc6d6ebde5]
- RMPD      [Kernel Density Estimation] [Question 3 - I3] [2012-10-16 12:10:16] [90f4fc95bc23bd40c615363dd079f863] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
15
18
11
8
19
4
20
16
14
10
13
14
8
23
11
9
24
5
15
5
19
6
13
11
17
17
5
9
15
17
17
20
12
7
16
7
14
24
15
15
10
14
18
12
9
9
8
18
10
17
14
16
10
19
10
14
10
4
19
9
12
16
11
18
11
24
17
18
9
19
18
12
23
22
14
14
16
23
7
10
12
12
12
17
21
16
11
14
13
9
19
13
19
13
13
13
14
12
22
11
5
18
19
14
15
12
19
15
17
8
10
12
12
20
12
12
14
6
10
18
18
7
18
9
17
22
11
15
17
15
22
9
13
20
14
14
12
20
20
8
17
9
18
22
10
13
15
18
18
12
12
20
12
16
16
18
16
13
17
13
17

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178631&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178631&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178631&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'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth1.49677288919099
#Observations162

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.49677288919099 \tabularnewline
#Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178631&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.49677288919099[/C][/ROW]
[ROW][C]#Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178631&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178631&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
Bandwidth1.49677288919099
#Observations162






Maximum Density Values
Kernelx-valuemax. density
Gaussian12.89408526803260.0764928589750117
Epanechnikov13.00751242002920.0754871688245587
Rectangular14.48206539598580.0880988367191382
Triangular12.04338162805770.076229403793684
Biweight12.95079884403090.0754808655473366
Cosine12.78065811603590.0755952306266494
Optcosine12.95079884403090.075613157988229

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 12.8940852680326 & 0.0764928589750117 \tabularnewline
Epanechnikov & 13.0075124200292 & 0.0754871688245587 \tabularnewline
Rectangular & 14.4820653959858 & 0.0880988367191382 \tabularnewline
Triangular & 12.0433816280577 & 0.076229403793684 \tabularnewline
Biweight & 12.9507988440309 & 0.0754808655473366 \tabularnewline
Cosine & 12.7806581160359 & 0.0755952306266494 \tabularnewline
Optcosine & 12.9507988440309 & 0.075613157988229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178631&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]12.8940852680326[/C][C]0.0764928589750117[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]13.0075124200292[/C][C]0.0754871688245587[/C][/ROW]
[ROW][C]Rectangular[/C][C]14.4820653959858[/C][C]0.0880988367191382[/C][/ROW]
[ROW][C]Triangular[/C][C]12.0433816280577[/C][C]0.076229403793684[/C][/ROW]
[ROW][C]Biweight[/C][C]12.9507988440309[/C][C]0.0754808655473366[/C][/ROW]
[ROW][C]Cosine[/C][C]12.7806581160359[/C][C]0.0755952306266494[/C][/ROW]
[ROW][C]Optcosine[/C][C]12.9507988440309[/C][C]0.075613157988229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178631&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178631&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
Gaussian12.89408526803260.0764928589750117
Epanechnikov13.00751242002920.0754871688245587
Rectangular14.48206539598580.0880988367191382
Triangular12.04338162805770.076229403793684
Biweight12.95079884403090.0754808655473366
Cosine12.78065811603590.0755952306266494
Optcosine12.95079884403090.075613157988229


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')
}