FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationWed, 17 Dec 2014 09:32:30 +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/17/t14188087653yxwv1klo444du1.htm/, Retrieved Thu, 16 May 2024 20:08:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270004, Retrieved Thu, 16 May 2024 20:08:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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] [] [2014-12-17 09:30:34] [6b382800c0d3804662889dbce999b8c7]
- R  D        [Kernel Density Estimation] [] [2014-12-17 09:32:30] [6993448de96b8662e47595bfdf466bf3] [Current]
-    D          [Kernel Density Estimation] [] [2014-12-17 09:33:30] [6b382800c0d3804662889dbce999b8c7]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8
18
12
24
16
19
16
15
28
21
18
22
19
22
25
20
16
19
18
26
24
20
19
19
23
18
16
18
21
20
15
19
19
7
20
20
19
19
20
18
14
17
17
8
9
22
20
20
22
22
22
16
14
24
21
20
20
18
14
19
24
19
16
16
16
14
22
21
15
14
15
14
20
21
14
19
16
13
26
13
18
15
18
21
17
18
20
18
25
20
19
18
12
22
16
18
23
20
20
16
22
19
23
6
19
24
19
15
18
18
22
23
18
17
6
22
20
16
16
17
20
23
18
13
22
20
20
13
16
25
16
15
19
19
24
9
22
15
22
22
24
12
21
25
26
21
14
28
21
16
16
25
21
22
9
20
19
24
22
22
12
17
18
10
22
24
18
18
23
21
21
28
17
21
21
20
18
17
7
17
14
18
14
23
20
14
17
21
23
24
21
14
24
16
21
8
17
18
17
16
22
17
21
20
20
19
8
19
11
13
18
19
23
20
22
19
16
11
21
14
21
20
21
20
19
19
18
20
21
22
19
23
16
23
18
23
20
20
23
13
21
26
18
19
18
18
19
13
10
21
24
21
23
18
11
16
20
20
26
21
12
15
18
14
18
16
19
7
21
24
21
20
22
17
19
20
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'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=270004&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=270004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270004&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
Bandwidth1.08889718419459
#Observations279

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.08889718419459 \tabularnewline
#Observations & 279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270004&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.08889718419459[/C][/ROW]
[ROW][C]#Observations[/C][C]279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270004&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
Bandwidth1.08889718419459
#Observations279






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.37312873183880.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5964820242471 & 0.111269388019177 \tabularnewline
Epanechnikov & 19.8756736397576 & 0.112197638606549 \tabularnewline
Rectangular & 19.3731287318388 & 0.118775895097344 \tabularnewline
Triangular & 19.9873502859618 & 0.113746281974634 \tabularnewline
Biweight & 19.6523203473492 & 0.111365550220941 \tabularnewline
Cosine & 19.5964820242471 & 0.111386498980232 \tabularnewline
Optcosine & 19.8756736397576 & 0.111959374434935 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270004&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]19.5964820242471[/C][C]0.111269388019177[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.8756736397576[/C][C]0.112197638606549[/C][/ROW]
[ROW][C]Rectangular[/C][C]19.3731287318388[/C][C]0.118775895097344[/C][/ROW]
[ROW][C]Triangular[/C][C]19.9873502859618[/C][C]0.113746281974634[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6523203473492[/C][C]0.111365550220941[/C][/ROW]
[ROW][C]Cosine[/C][C]19.5964820242471[/C][C]0.111386498980232[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8756736397576[/C][C]0.111959374434935[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270004&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270004&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
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.37312873183880.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.42896705494090.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5964820242471 & 0.111269388019177 \tabularnewline
Epanechnikov & 19.8756736397576 & 0.112197638606549 \tabularnewline
Rectangular & 19.4289670549409 & 0.118775895097344 \tabularnewline
Triangular & 19.9873502859618 & 0.113746281974634 \tabularnewline
Biweight & 19.6523203473492 & 0.111365550220941 \tabularnewline
Cosine & 19.5964820242471 & 0.111386498980232 \tabularnewline
Optcosine & 19.8756736397576 & 0.111959374434935 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270004&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]19.5964820242471[/C][C]0.111269388019177[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.8756736397576[/C][C]0.112197638606549[/C][/ROW]
[ROW][C]Rectangular[/C][C]19.4289670549409[/C][C]0.118775895097344[/C][/ROW]
[ROW][C]Triangular[/C][C]19.9873502859618[/C][C]0.113746281974634[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6523203473492[/C][C]0.111365550220941[/C][/ROW]
[ROW][C]Cosine[/C][C]19.5964820242471[/C][C]0.111386498980232[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8756736397576[/C][C]0.111959374434935[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270004&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270004&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
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.42896705494090.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.59648202424710.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5964820242471 & 0.111269388019177 \tabularnewline
Epanechnikov & 19.8756736397576 & 0.112197638606549 \tabularnewline
Rectangular & 19.5964820242471 & 0.118775895097344 \tabularnewline
Triangular & 19.9873502859618 & 0.113746281974634 \tabularnewline
Biweight & 19.6523203473492 & 0.111365550220941 \tabularnewline
Cosine & 19.5964820242471 & 0.111386498980232 \tabularnewline
Optcosine & 19.8756736397576 & 0.111959374434935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270004&T=4

[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]19.5964820242471[/C][C]0.111269388019177[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.8756736397576[/C][C]0.112197638606549[/C][/ROW]
[ROW][C]Rectangular[/C][C]19.5964820242471[/C][C]0.118775895097344[/C][/ROW]
[ROW][C]Triangular[/C][C]19.9873502859618[/C][C]0.113746281974634[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6523203473492[/C][C]0.111365550220941[/C][/ROW]
[ROW][C]Cosine[/C][C]19.5964820242471[/C][C]0.111386498980232[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8756736397576[/C][C]0.111959374434935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270004&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270004&T=4

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
Gaussian19.59648202424710.111269388019177
Epanechnikov19.87567363975760.112197638606549
Rectangular19.59648202424710.118775895097344
Triangular19.98735028596180.113746281974634
Biweight19.65232034734920.111365550220941
Cosine19.59648202424710.111386498980232
Optcosine19.87567363975760.111959374434935


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')
}