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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 14:58:44 +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/t1418655536z6wa6qxc9y3zfmr.htm/, Retrieved Thu, 16 May 2024 14:21:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268572, Retrieved Thu, 16 May 2024 14:21:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
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 IM3] [2014-12-15 14:58:44] [9636d26fd774798d33054b538c301d75] [Current]
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Dataseries X:
7
18
20
9
19
12
16
17
9
28
20
16
22
17
12
18
20
12
16
16
21
15
17
17
17
18
15
20
13
21
12
6
13
6
19
12
14
13
12
17
19
10
10
11
11
10
7
22
12
18
20
9
16
14
11
20
17
14
8
16
11
10
15
15
10
10
18
10
22
16
10
7
16
16
16
22
13
5
10
8
16
8
16
14
15
9
21
7
17
18
16
16
14
15
8
22
5
13
22
18
15
11
19
19
21
4
17
10
13
15
11
20
13
18
20
15
4
9
18
12
17
12
16
17
14
13
20
16
15
10
16
21
15
16
19
9
19
7
23
14
10
16
12
10
7
20
9
14
12
10
19
16
11
15
14
11
14
15
7
22
19
22
11
19
9
11
17
12
17
10
17
13
11
19
21
24
13
16
13
15
15
11
7
13
13
12
8
7
17
9
18
17
17
18
12
14
22
19
21
10
16
11
15
12
21
22
20
15
9
15
14
11
9
18
12
11
14
10
18
11
14
16
11
8
16
13
12
17
23
14
10
16
11
16
19
17
12
17
11
19
12
8
17
13
17
7
23
18
13
17
13
13
8
16
14
13
19
15
15
8
14
7
11
17
19
17
12
12
18
16
15
20
16
12
10
28
19
18
19
8
17
16
18
12
17
13




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268572&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]3 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=268572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268572&T=0

As an alternative you can also use a 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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Properties of Density Trace
Bandwidth1.27465253414803
#Observations286

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.27465253414803 \tabularnewline
#Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268572&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.27465253414803[/C][/ROW]
[ROW][C]#Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268572&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth1.27465253414803
#Observations286







Maximum Density Values
Kernelx-valuemax. density
Gaussian16.21676654249920.0855314929905283
Epanechnikov16.46449973392690.0835975663341907
Rectangular15.04003388321770.0910645551620762
Triangular16.03096664892850.0851701000960998
Biweight16.34063313821310.0838008494904808
Cosine16.21676654249920.0840973575753391
Optcosine16.46449973392690.0837972372457709

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 16.2167665424992 & 0.0855314929905283 \tabularnewline
Epanechnikov & 16.4644997339269 & 0.0835975663341907 \tabularnewline
Rectangular & 15.0400338832177 & 0.0910645551620762 \tabularnewline
Triangular & 16.0309666489285 & 0.0851701000960998 \tabularnewline
Biweight & 16.3406331382131 & 0.0838008494904808 \tabularnewline
Cosine & 16.2167665424992 & 0.0840973575753391 \tabularnewline
Optcosine & 16.4644997339269 & 0.0837972372457709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268572&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]16.2167665424992[/C][C]0.0855314929905283[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]16.4644997339269[/C][C]0.0835975663341907[/C][/ROW]
[ROW][C]Rectangular[/C][C]15.0400338832177[/C][C]0.0910645551620762[/C][/ROW]
[ROW][C]Triangular[/C][C]16.0309666489285[/C][C]0.0851701000960998[/C][/ROW]
[ROW][C]Biweight[/C][C]16.3406331382131[/C][C]0.0838008494904808[/C][/ROW]
[ROW][C]Cosine[/C][C]16.2167665424992[/C][C]0.0840973575753391[/C][/ROW]
[ROW][C]Optcosine[/C][C]16.4644997339269[/C][C]0.0837972372457709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268572&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268572&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian16.21676654249920.0855314929905283
Epanechnikov16.46449973392690.0835975663341907
Rectangular15.04003388321770.0910645551620762
Triangular16.03096664892850.0851701000960998
Biweight16.34063313821310.0838008494904808
Cosine16.21676654249920.0840973575753391
Optcosine16.46449973392690.0837972372457709



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')
}