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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 computationWed, 03 Dec 2014 18:59:18 +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/03/t14176331800btd7ossz2vymx2.htm/, Retrieved Thu, 16 May 2024 16:41:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=263025, Retrieved Thu, 16 May 2024 16:41:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2014-10-27 22:07:41] [8f0f7d8870e334acea674e48ede2c797]
- RMPD    [Kernel Density Estimation] [Kernel Density Plot] [2014-12-03 18:59:18] [310e7528d8f6aa5642dc98f4186768d1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
26
51
57
37
67
43
52
52
43
84
67
49
70
52
58
68
62
43
56
56
74
65
63
58
57
63
53
57
51
64
53
29
54
51
58
43
51
53
54
56
61
47
39
48
50
35
30
68
49
61
67
47
56
50
43
67
62
57
41
54
45
48
61
56
41
43
53
44
66
58
46
37
51
51
56
66
45
37
59
42
38
66
34
53
49
55
49
59
40
58
60
63
56
54
52
34
69
32
48
67
58
57
42
64
58
66
26
61
52
51
55
50
60
56
63
61
52
16
46
56
52
55
50
59
60
52
44
67
52
55
37
54
72
51
48
60
50
63
33
67
46
54
59
61
33
47
69
52
55
55
41
73
51
52
50
51
60
56
56
29
66
66
73
55
64
40
46
58
43
61
51
50
52
54
66
61
80
51
56
56
56
53
47
25
47
46
50
39
51
58
35
58
60
62
63
53
46
67
59
64
38
50
48
48
47
66
47
63
58
44
51
43
55
38
56
45
50
54
57
60
55
56
49
37
43
59
46
51
58
64
53
48
51
47
59
62
62
51
64
52
67
50
54
58
56
63
31
65
71
50
57
47
54
47
57
43
41
63
63
56
51
50
22
41
59
56
66
53
42
52
54
44
62
53
50
36
76
66
62
59
47
55
58
60
44
57
45
58
51
57
30
46
51
56
58
44
14
53
42
49
44
62
30
46
56
50
54
48
55
35
55
41
59
54
66
55
45
51
47
42
53
53
41
55
55
46
63
43
65
59
39
44
60
57
67
52
52
69
46
46
53
40
70
54
77
45
60
47
50
66
60
41
53
34
51
69
60
45
58
39
51
52
49
63
44
51
52
60
53
53
52
31
51
65
51
49
61
58
62
54
52
72
50
65
53
56
63
62
66
50
45
58
52
53
68
59
58
52
45
58
70
69
71
46
58
39
46
64
67
44
54
41
68
63
57
61
39
69
64
38
59
51
59
51
65
47
50
57
21
47
51
37
67
43
58
51
40
41
58
64
64
58
50
59
55
59
58
41
56
63
77
60
58
64
47
46
62
60
50
46
44
58
56
43
54
54
56
65
66
62
58
67
25
56
53
56
59
46
49
56
76
33
49
53
58
72
51
42
69
51
54
52
59
51
67
64
58

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263025&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263025&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth2.52237576836007
#Observations497

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.52237576836007 \tabularnewline
#Observations & 497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263025&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.52237576836007[/C][/ROW]
[ROW][C]#Observations[/C][C]497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263025&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
Bandwidth2.52237576836007
#Observations497






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular53.91479552054740.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0817793306241 & 0.0428860912198516 \tabularnewline
Epanechnikov & 54.0813987585321 & 0.0439813040641824 \tabularnewline
Rectangular & 53.9147955205474 & 0.0472059849578891 \tabularnewline
Triangular & 54.0813987585321 & 0.0431359406652521 \tabularnewline
Biweight & 54.0813987585321 & 0.043421435723736 \tabularnewline
Cosine & 54.0813987585321 & 0.0432527336714547 \tabularnewline
Optcosine & 54.4146052345014 & 0.0437768949530923 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263025&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]53.0817793306241[/C][C]0.0428860912198516[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0813987585321[/C][C]0.0439813040641824[/C][/ROW]
[ROW][C]Rectangular[/C][C]53.9147955205474[/C][C]0.0472059849578891[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0813987585321[/C][C]0.0431359406652521[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0813987585321[/C][C]0.043421435723736[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0813987585321[/C][C]0.0432527336714547[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4146052345014[/C][C]0.0437768949530923[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263025&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263025&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
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular53.91479552054740.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular54.08139875853210.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0817793306241 & 0.0428860912198516 \tabularnewline
Epanechnikov & 54.0813987585321 & 0.0439813040641824 \tabularnewline
Rectangular & 54.0813987585321 & 0.0472059849578891 \tabularnewline
Triangular & 54.0813987585321 & 0.0431359406652521 \tabularnewline
Biweight & 54.0813987585321 & 0.043421435723736 \tabularnewline
Cosine & 54.0813987585321 & 0.0432527336714547 \tabularnewline
Optcosine & 54.4146052345014 & 0.0437768949530923 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263025&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]53.0817793306241[/C][C]0.0428860912198516[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0813987585321[/C][C]0.0439813040641824[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.0813987585321[/C][C]0.0472059849578891[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0813987585321[/C][C]0.0431359406652521[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0813987585321[/C][C]0.043421435723736[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0813987585321[/C][C]0.0432527336714547[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4146052345014[/C][C]0.0437768949530923[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263025&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263025&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
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular54.08139875853210.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular54.24800199651670.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0817793306241 & 0.0428860912198516 \tabularnewline
Epanechnikov & 54.0813987585321 & 0.0439813040641824 \tabularnewline
Rectangular & 54.2480019965167 & 0.0472059849578891 \tabularnewline
Triangular & 54.0813987585321 & 0.0431359406652521 \tabularnewline
Biweight & 54.0813987585321 & 0.043421435723736 \tabularnewline
Cosine & 54.0813987585321 & 0.0432527336714547 \tabularnewline
Optcosine & 54.4146052345014 & 0.0437768949530923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=263025&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]53.0817793306241[/C][C]0.0428860912198516[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0813987585321[/C][C]0.0439813040641824[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.2480019965167[/C][C]0.0472059849578891[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0813987585321[/C][C]0.0431359406652521[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0813987585321[/C][C]0.043421435723736[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0813987585321[/C][C]0.0432527336714547[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4146052345014[/C][C]0.0437768949530923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=263025&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=263025&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
Gaussian53.08177933062410.0428860912198516
Epanechnikov54.08139875853210.0439813040641824
Rectangular54.24800199651670.0472059849578891
Triangular54.08139875853210.0431359406652521
Biweight54.08139875853210.043421435723736
Cosine54.08139875853210.0432527336714547
Optcosine54.41460523450140.0437768949530923


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')
}