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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 14:10:13 +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/t1418652619b97e9srduq17orl.htm/, Retrieved Sun, 19 May 2024 13:03:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268449, Retrieved Sun, 19 May 2024 13:03:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

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] [] [2014-12-15 14:10:13] [d043def4c969c6fe6dac6c6c71a7875a] [Current]
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Dataset

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

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'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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268449&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268449&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'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth1.200904558419
#Observations171

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.200904558419 \tabularnewline
#Observations & 171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268449&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.200904558419[/C][/ROW]
[ROW][C]#Observations[/C][C]171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268449&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
Bandwidth1.200904558419
#Observations171






Maximum Density Values
Kernelx-valuemax. density
Gaussian23.82984064263490.116562600850034
Epanechnikov24.05845455535910.115488546639781
Rectangular22.97253846991920.136356707942018
Triangular24.0013010771780.116276614385901
Biweight23.71553368627280.115262883998793
Cosine23.77268716445380.115560148069786
Optcosine24.05845455535910.115130433609341

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 23.8298406426349 & 0.116562600850034 \tabularnewline
Epanechnikov & 24.0584545553591 & 0.115488546639781 \tabularnewline
Rectangular & 22.9725384699192 & 0.136356707942018 \tabularnewline
Triangular & 24.001301077178 & 0.116276614385901 \tabularnewline
Biweight & 23.7155336862728 & 0.115262883998793 \tabularnewline
Cosine & 23.7726871644538 & 0.115560148069786 \tabularnewline
Optcosine & 24.0584545553591 & 0.115130433609341 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268449&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]23.8298406426349[/C][C]0.116562600850034[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]24.0584545553591[/C][C]0.115488546639781[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.9725384699192[/C][C]0.136356707942018[/C][/ROW]
[ROW][C]Triangular[/C][C]24.001301077178[/C][C]0.116276614385901[/C][/ROW]
[ROW][C]Biweight[/C][C]23.7155336862728[/C][C]0.115262883998793[/C][/ROW]
[ROW][C]Cosine[/C][C]23.7726871644538[/C][C]0.115560148069786[/C][/ROW]
[ROW][C]Optcosine[/C][C]24.0584545553591[/C][C]0.115130433609341[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268449&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268449&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
Gaussian23.82984064263490.116562600850034
Epanechnikov24.05845455535910.115488546639781
Rectangular22.97253846991920.136356707942018
Triangular24.0013010771780.116276614385901
Biweight23.71553368627280.115262883998793
Cosine23.77268716445380.115560148069786
Optcosine24.05845455535910.115130433609341






Maximum Density Values
Kernelx-valuemax. density
Gaussian23.82984064263490.116562600850034
Epanechnikov24.05845455535910.115488546639781
Rectangular23.02969194810030.136356707942018
Triangular24.0013010771780.116276614385901
Biweight23.71553368627280.115262883998793
Cosine23.77268716445380.115560148069786
Optcosine24.05845455535910.115130433609341

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 23.8298406426349 & 0.116562600850034 \tabularnewline
Epanechnikov & 24.0584545553591 & 0.115488546639781 \tabularnewline
Rectangular & 23.0296919481003 & 0.136356707942018 \tabularnewline
Triangular & 24.001301077178 & 0.116276614385901 \tabularnewline
Biweight & 23.7155336862728 & 0.115262883998793 \tabularnewline
Cosine & 23.7726871644538 & 0.115560148069786 \tabularnewline
Optcosine & 24.0584545553591 & 0.115130433609341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268449&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]23.8298406426349[/C][C]0.116562600850034[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]24.0584545553591[/C][C]0.115488546639781[/C][/ROW]
[ROW][C]Rectangular[/C][C]23.0296919481003[/C][C]0.136356707942018[/C][/ROW]
[ROW][C]Triangular[/C][C]24.001301077178[/C][C]0.116276614385901[/C][/ROW]
[ROW][C]Biweight[/C][C]23.7155336862728[/C][C]0.115262883998793[/C][/ROW]
[ROW][C]Cosine[/C][C]23.7726871644538[/C][C]0.115560148069786[/C][/ROW]
[ROW][C]Optcosine[/C][C]24.0584545553591[/C][C]0.115130433609341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268449&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268449&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
Gaussian23.82984064263490.116562600850034
Epanechnikov24.05845455535910.115488546639781
Rectangular23.02969194810030.136356707942018
Triangular24.0013010771780.116276614385901
Biweight23.71553368627280.115262883998793
Cosine23.77268716445380.115560148069786
Optcosine24.05845455535910.115130433609341


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
}