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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 13:39:02 +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/t14188235500a5alvfqqafok2f.htm/, Retrieved Thu, 16 May 2024 20:02:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270237, Retrieved Thu, 16 May 2024 20:02:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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 13:39:02] [7de19aadd459682308988067914fc05d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
50
68
62
54
71
54
65
73
52
84
42
66
65
78
73
75
72
66
70
61
81
71
69
71
72
68
70
68
61
67
76
70
60
77
72
69
71
62
70
64
58
76
52
59
68
76
65
67
59
69
76
63
75
63
60
73
63
70
75
66
63
63
64
70
75
61
60
62
73
61
66
64
59
64
60
56
66
78
53
67
59
66
68
71
66
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72
71
59
64
66
78
68
73
62
65
68
65
60
71
65
68
64
74
69
76
68
72
67
63
59
73
66
62
69
66
51
56
67
69
57
56
55
63
67
65
47
76
64
68
64
65
71
63
60
68
72
70
61
61
62
71
71
51
56
70
73
76
59
68
48
52
59
60
59
57
79
60
60
59
62
59
61
71
57
66
63
69
58
59
48
66
73
67
61
68
75
62
69
58
60
74
55
62
63
69
58
58
68
72
62
62
65
69
66
72
62
75
58
66
55
47
72
62
64
64
19
50
68
70
79
69
71
48
66
73
74
66
71
74
78
75
53
60
50
70
69
65
78
78
59
72
70
63
63
71
74
67
66
62
80
73
67
61
73
74
32
69
69
84
64
58
60
59
78
57
60
68
68
73
69
67
60
65
66
74
81
72
55
49
74
53
64
65
57
51
80
67
70
74
75
70
69
65
55
71
65
69
48
69
68
74
67
65
63
74
39
68
69
68
63
67
70
68
66
70
78
59
62
75
74
73
62
69
65
67
73
52
61
53
63
78
65
77
69
68
76
63
41
76
67
69
59
73
72
52
65
63
78
56
68
56
64
68
75
67
55
73
66
75
77
65
75
57
61
71
72
62
66
66
63
60
64
74
59
71
69
63
73
55
77
70
64
78
60
66
77
68
78
68
60
65
64
69
72
50
72
71
80
74
64
69
76
75
79
73
60
76
55
53
62
69
78
68
67
75
59
73
70
59
64
63
67
58
71
79
53
76
66
64
57
67
72
58
74
57
62
74
54
62
66
64
74
71
66
66
63
65
70
66
66
78
77
72
65
67
72
58
84
67
84
58
63
75
55
72
58
69
54
58
67
77
80
67
75
71
72
75
79
76
72
81
52
76
60
72
77
64
67
72
79
40
71
73
75
70
66
66
73
74
58
51
75
70
50
64
77
71

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270237&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270237&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270237&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'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth1.93950919338869
#Observations498

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.93950919338869 \tabularnewline
#Observations & 498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270237&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.93950919338869[/C][/ROW]
[ROW][C]#Observations[/C][C]498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270237&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270237&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
Bandwidth1.93950919338869
#Observations498






Maximum Density Values
Kernelx-valuemax. density
Gaussian67.17235276762170.0510821213464365
Epanechnikov67.0223780999890.0507378761037037
Rectangular68.97204877921470.0523029567044356
Triangular67.0223780999890.0508840112475649
Biweight67.32232743525450.0507804766293375
Cosine67.32232743525450.0508319523858768
Optcosine67.0223780999890.0508219636619597

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 67.1723527676217 & 0.0510821213464365 \tabularnewline
Epanechnikov & 67.022378099989 & 0.0507378761037037 \tabularnewline
Rectangular & 68.9720487792147 & 0.0523029567044356 \tabularnewline
Triangular & 67.022378099989 & 0.0508840112475649 \tabularnewline
Biweight & 67.3223274352545 & 0.0507804766293375 \tabularnewline
Cosine & 67.3223274352545 & 0.0508319523858768 \tabularnewline
Optcosine & 67.022378099989 & 0.0508219636619597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270237&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]67.1723527676217[/C][C]0.0510821213464365[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]67.022378099989[/C][C]0.0507378761037037[/C][/ROW]
[ROW][C]Rectangular[/C][C]68.9720487792147[/C][C]0.0523029567044356[/C][/ROW]
[ROW][C]Triangular[/C][C]67.022378099989[/C][C]0.0508840112475649[/C][/ROW]
[ROW][C]Biweight[/C][C]67.3223274352545[/C][C]0.0507804766293375[/C][/ROW]
[ROW][C]Cosine[/C][C]67.3223274352545[/C][C]0.0508319523858768[/C][/ROW]
[ROW][C]Optcosine[/C][C]67.022378099989[/C][C]0.0508219636619597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270237&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270237&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
Gaussian67.17235276762170.0510821213464365
Epanechnikov67.0223780999890.0507378761037037
Rectangular68.97204877921470.0523029567044356
Triangular67.0223780999890.0508840112475649
Biweight67.32232743525450.0507804766293375
Cosine67.32232743525450.0508319523858768
Optcosine67.0223780999890.0508219636619597


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')
}