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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, 17 Dec 2014 13:35:58 +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/t1418823370kb7vi36txv2wlv4.htm/, Retrieved Thu, 16 May 2024 08:55:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270230, Retrieved Thu, 16 May 2024 08:55:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Survey Scores] [Summary Mean Vs. ...] [2014-12-15 09:53:50] [69bf0eb8b9b38defaaf4848d8c317571]
- RMPD    [Kernel Density Estimation] [] [2014-12-17 13:35:58] [7de19aadd459682308988067914fc05d] [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
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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
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48
61
56
41
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44
66
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46
37
51
51
56
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45
37
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42
38
66
34
53
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40
58
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63
56
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34
69
32
48
67
58
57
42
64
58
66
26
61
52
51
55
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61
52
16
46
56
52
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59
60
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44
67
52
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37
54
72
51
48
60
50
63
33
67
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54
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61
33
47
69
52
55
55
41
73
51
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50
51
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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
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63
53
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67
59
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38
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66
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63
58
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51
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55
38
56
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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
53

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270230&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270230&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270230&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'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth2.52136195140529
#Observations498

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.52136195140529 \tabularnewline
#Observations & 498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270230&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.52136195140529[/C][/ROW]
[ROW][C]#Observations[/C][C]498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270230&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270230&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
Bandwidth2.52136195140529
#Observations498






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular53.91444435498770.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0814876846508 & 0.0431191959377678 \tabularnewline
Epanechnikov & 54.0810356890551 & 0.0441527865498459 \tabularnewline
Rectangular & 53.9144443549877 & 0.0473600399169834 \tabularnewline
Triangular & 54.0810356890551 & 0.0433191202845553 \tabularnewline
Biweight & 54.0810356890551 & 0.043603243554558 \tabularnewline
Cosine & 54.0810356890551 & 0.0434385639218116 \tabularnewline
Optcosine & 54.4142183571899 & 0.0439420498780886 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270230&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]53.0814876846508[/C][C]0.0431191959377678[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0810356890551[/C][C]0.0441527865498459[/C][/ROW]
[ROW][C]Rectangular[/C][C]53.9144443549877[/C][C]0.0473600399169834[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0810356890551[/C][C]0.0433191202845553[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0810356890551[/C][C]0.043603243554558[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0810356890551[/C][C]0.0434385639218116[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4142183571899[/C][C]0.0439420498780886[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270230&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270230&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
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular53.91444435498770.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular54.08103568905510.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0814876846508 & 0.0431191959377678 \tabularnewline
Epanechnikov & 54.0810356890551 & 0.0441527865498459 \tabularnewline
Rectangular & 54.0810356890551 & 0.0473600399169834 \tabularnewline
Triangular & 54.0810356890551 & 0.0433191202845553 \tabularnewline
Biweight & 54.0810356890551 & 0.043603243554558 \tabularnewline
Cosine & 54.0810356890551 & 0.0434385639218116 \tabularnewline
Optcosine & 54.4142183571899 & 0.0439420498780886 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270230&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]53.0814876846508[/C][C]0.0431191959377678[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0810356890551[/C][C]0.0441527865498459[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.0810356890551[/C][C]0.0473600399169834[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0810356890551[/C][C]0.0433191202845553[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0810356890551[/C][C]0.043603243554558[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0810356890551[/C][C]0.0434385639218116[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4142183571899[/C][C]0.0439420498780886[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270230&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270230&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
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular54.08103568905510.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular54.24762702312250.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.0814876846508 & 0.0431191959377678 \tabularnewline
Epanechnikov & 54.0810356890551 & 0.0441527865498459 \tabularnewline
Rectangular & 54.2476270231225 & 0.0473600399169834 \tabularnewline
Triangular & 54.0810356890551 & 0.0433191202845553 \tabularnewline
Biweight & 54.0810356890551 & 0.043603243554558 \tabularnewline
Cosine & 54.0810356890551 & 0.0434385639218116 \tabularnewline
Optcosine & 54.4142183571899 & 0.0439420498780886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270230&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]53.0814876846508[/C][C]0.0431191959377678[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0810356890551[/C][C]0.0441527865498459[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.2476270231225[/C][C]0.0473600399169834[/C][/ROW]
[ROW][C]Triangular[/C][C]54.0810356890551[/C][C]0.0433191202845553[/C][/ROW]
[ROW][C]Biweight[/C][C]54.0810356890551[/C][C]0.043603243554558[/C][/ROW]
[ROW][C]Cosine[/C][C]54.0810356890551[/C][C]0.0434385639218116[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.4142183571899[/C][C]0.0439420498780886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270230&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270230&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
Gaussian53.08148768465080.0431191959377678
Epanechnikov54.08103568905510.0441527865498459
Rectangular54.24762702312250.0473600399169834
Triangular54.08103568905510.0433191202845553
Biweight54.08103568905510.043603243554558
Cosine54.08103568905510.0434385639218116
Optcosine54.41421835718990.0439420498780886


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')
}