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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 computationMon, 15 Dec 2014 15:16:10 +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/t14186565806073va864x1zqbm.htm/, Retrieved Thu, 16 May 2024 08:32:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268617, Retrieved Thu, 16 May 2024 08:32:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62

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] [Gaussian EM] [2014-12-15 15:16:10] [9636d26fd774798d33054b538c301d75] [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
67
59
66
68
71
66
73
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

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=268617&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=268617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268617&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
Bandwidth2.16702790822554
#Observations286

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.16702790822554 \tabularnewline
#Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268617&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.16702790822554[/C][/ROW]
[ROW][C]#Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268617&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
Bandwidth2.16702790822554
#Observations286






Maximum Density Values
Kernelx-valuemax. density
Gaussian67.75681180695910.0510571522947789
Epanechnikov67.45151956645290.0510664365628557
Rectangular67.6041656867060.0540302315357547
Triangular68.06210404746540.0512790376440325
Biweight67.90945792721230.050975789186989
Cosine67.75681180695910.0509820899665453
Optcosine67.45151956645290.0510627484282962

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 67.7568118069591 & 0.0510571522947789 \tabularnewline
Epanechnikov & 67.4515195664529 & 0.0510664365628557 \tabularnewline
Rectangular & 67.604165686706 & 0.0540302315357547 \tabularnewline
Triangular & 68.0621040474654 & 0.0512790376440325 \tabularnewline
Biweight & 67.9094579272123 & 0.050975789186989 \tabularnewline
Cosine & 67.7568118069591 & 0.0509820899665453 \tabularnewline
Optcosine & 67.4515195664529 & 0.0510627484282962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268617&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]67.7568118069591[/C][C]0.0510571522947789[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]67.4515195664529[/C][C]0.0510664365628557[/C][/ROW]
[ROW][C]Rectangular[/C][C]67.604165686706[/C][C]0.0540302315357547[/C][/ROW]
[ROW][C]Triangular[/C][C]68.0621040474654[/C][C]0.0512790376440325[/C][/ROW]
[ROW][C]Biweight[/C][C]67.9094579272123[/C][C]0.050975789186989[/C][/ROW]
[ROW][C]Cosine[/C][C]67.7568118069591[/C][C]0.0509820899665453[/C][/ROW]
[ROW][C]Optcosine[/C][C]67.4515195664529[/C][C]0.0510627484282962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268617&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268617&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
Gaussian67.75681180695910.0510571522947789
Epanechnikov67.45151956645290.0510664365628557
Rectangular67.6041656867060.0540302315357547
Triangular68.06210404746540.0512790376440325
Biweight67.90945792721230.050975789186989
Cosine67.75681180695910.0509820899665453
Optcosine67.45151956645290.0510627484282962


Figures (Output of Computation)

Input Parameters & R Code

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')
}