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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, 15 Dec 2014 14:52:00 +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/15/t1418655152o5pdcrpmxyo90gd.htm/, Retrieved Sun, 19 May 2024 14:43:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268551, Retrieved Sun, 19 May 2024 14:43:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Maximum-likelihood Fitting - Normal Distribution] [Intrinsic Motivat...] [2010-10-12 11:57:21] [b98453cac15ba1066b407e146608df68]
- RMP   [Maximum-likelihood Fitting - Normal Distribution] [] [2014-10-14 18:01:50] [32b17a345b130fdf5cc88718ed94a974]
- RMPD      [Kernel Density Estimation] [Gaussian IM1] [2014-12-15 14:52:00] [9636d26fd774798d33054b538c301d75] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
11
15
19
16
24
15
17
19
19
28
26
15
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16
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15
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8
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21
16
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21
20
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15
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17
24
13
19
20
22
19
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15
21
24
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21
19
14
25
11
17
22
20
22
15
23
20
22
16
25
18
19
25
21
22
21
22
23
20
6
15
18
24
22
21
23
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20
18
25
16
20
14
22
26
20
17
22
22
20
17
22
17
22
21
25
11
19
24
17
22
22
17
26
19
20
19
21
24
21
19
13
24
28
27
22
23
19
18
23
21
22
17
15
21
20
26
19
28
21
19
22
21
20
19
11
17
19
20
17
21
21
12
23
22
22
21
20
18
21
24
22
20
17
19
16
19
23
8
22
23
15
17
21
25
18
23
20
21
21
24
22
22
23
17
15
24
22
19
18
21
20
19
19
16
18
23
22
23
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24
25
25
20
23
21
23
23
11
21
27
19
21
16
22
21
22
16
18
23
24
20
20
18
4
14
22
17
23
20
18
19
20
15
24
21
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19
27
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23
20
17
21
23
22
16
20
16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268551&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268551&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth0.866811163290217
#Observations286

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.866811163290217 \tabularnewline
#Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268551&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.866811163290217[/C][/ROW]
[ROW][C]#Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268551&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
Bandwidth0.866811163290217
#Observations286






Maximum Density Values
Kernelx-valuemax. density
Gaussian21.22872667054080.126568219872045
Epanechnikov21.400160331870.129602776300623
Rectangular20.48584747144750.143259787478809
Triangular21.00014845543520.12940745612127
Biweight21.34301577809360.127512293346762
Cosine21.1144375629880.127340999003043
Optcosine21.34301577809360.128992116635315

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 21.2287266705408 & 0.126568219872045 \tabularnewline
Epanechnikov & 21.40016033187 & 0.129602776300623 \tabularnewline
Rectangular & 20.4858474714475 & 0.143259787478809 \tabularnewline
Triangular & 21.0001484554352 & 0.12940745612127 \tabularnewline
Biweight & 21.3430157780936 & 0.127512293346762 \tabularnewline
Cosine & 21.114437562988 & 0.127340999003043 \tabularnewline
Optcosine & 21.3430157780936 & 0.128992116635315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268551&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]21.2287266705408[/C][C]0.126568219872045[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.40016033187[/C][C]0.129602776300623[/C][/ROW]
[ROW][C]Rectangular[/C][C]20.4858474714475[/C][C]0.143259787478809[/C][/ROW]
[ROW][C]Triangular[/C][C]21.0001484554352[/C][C]0.12940745612127[/C][/ROW]
[ROW][C]Biweight[/C][C]21.3430157780936[/C][C]0.127512293346762[/C][/ROW]
[ROW][C]Cosine[/C][C]21.114437562988[/C][C]0.127340999003043[/C][/ROW]
[ROW][C]Optcosine[/C][C]21.3430157780936[/C][C]0.128992116635315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268551&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268551&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
Gaussian21.22872667054080.126568219872045
Epanechnikov21.400160331870.129602776300623
Rectangular20.48584747144750.143259787478809
Triangular21.00014845543520.12940745612127
Biweight21.34301577809360.127512293346762
Cosine21.1144375629880.127340999003043
Optcosine21.34301577809360.128992116635315


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
}