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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, 19 Nov 2012 09:09:59 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/19/t1353334302zozomhzk37umpsg.htm/, Retrieved Sun, 28 Apr 2024 09:55:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190526, Retrieved Sun, 28 Apr 2024 09:55:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [Kernel Density ( ...] [2012-11-19 14:09:59] [164264d60f8cebcb0f9613bc1a0dee58] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
59
34
49
50
34
15
107
9
28
41
46
66
48
37
72
50
90
64
66
38
56
60
96
43
37
49
48
63
62
35
62
59
47
72
24
82
28
60
90
2
47
30
27
74
75
41
49
42
31
32
101
22
51
77
42
47
7
91
18
28
61
68
95
29
65
71
57
87
66
49
58
55
48
40
52
52
33
51
20
54
47
40
77
68
51
38
42
33
96
40
54
22
34
36
31
80
67
41
57
51
39
61
68
45
51
64
74
24
86
63
65
40
12
43
46
56
65
61
28
26
37
17
35
28
62
23
28
28
68
6
12
42
17
28
37
88
6
58
6
9
13
37
25
68
51
22
36
27
11
42
76
48
30
91
70
98
44
27
24
64
98
23
33
90
36
57
46
39
32
69
83
54
48
71
29
38
55
26
62
38
21
23
4
50
76
2
13
5
37
26
42
27
22
16
39
33
20
18
28
20
21
14
38
30
25
12
22
50
37
34
26
34
15
23
16
15
17
16
18
22
21
29
27
19
9
38
20
18
17
21
9
23
24
14
18
16
44
13
20
11
26
39
14
14
20
24
28
24
24
10
42
28
5
28
24
9
9
25
17
11
8
21
10
15
14
23
18
16
33
21
29
20
12
29
17
19
15
5
24
23
22
25
25
11
18
14
16
17
20

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190526&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]5 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=190526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190526&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth6.63497858653245
#Observations289

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 6.63497858653245 \tabularnewline
#Observations & 289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190526&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]6.63497858653245[/C][/ROW]
[ROW][C]#Observations[/C][C]289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190526&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
Bandwidth6.63497858653245
#Observations289






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular20.06869003995660.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.9025427115651 & 0.0196751303463845 \tabularnewline
Epanechnikov & 22.9025427115651 & 0.0191988709600782 \tabularnewline
Rectangular & 20.0686900399566 & 0.0189689177648908 \tabularnewline
Triangular & 23.185927978726 & 0.0194843188521844 \tabularnewline
Biweight & 22.9025427115651 & 0.0193710306536086 \tabularnewline
Cosine & 22.9025427115651 & 0.019422531203197 \tabularnewline
Optcosine & 23.185927978726 & 0.0192640613854086 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190526&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]22.9025427115651[/C][C]0.0196751303463845[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.9025427115651[/C][C]0.0191988709600782[/C][/ROW]
[ROW][C]Rectangular[/C][C]20.0686900399566[/C][C]0.0189689177648908[/C][/ROW]
[ROW][C]Triangular[/C][C]23.185927978726[/C][C]0.0194843188521844[/C][/ROW]
[ROW][C]Biweight[/C][C]22.9025427115651[/C][C]0.0193710306536086[/C][/ROW]
[ROW][C]Cosine[/C][C]22.9025427115651[/C][C]0.019422531203197[/C][/ROW]
[ROW][C]Optcosine[/C][C]23.185927978726[/C][C]0.0192640613854086[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190526&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
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular20.06869003995660.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular26.86993645181710.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.9025427115651 & 0.0196751303463845 \tabularnewline
Epanechnikov & 22.9025427115651 & 0.0191988709600782 \tabularnewline
Rectangular & 26.8699364518171 & 0.0189689177648908 \tabularnewline
Triangular & 23.185927978726 & 0.0194843188521844 \tabularnewline
Biweight & 22.9025427115651 & 0.0193710306536086 \tabularnewline
Cosine & 22.9025427115651 & 0.019422531203197 \tabularnewline
Optcosine & 23.185927978726 & 0.0192640613854086 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190526&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]22.9025427115651[/C][C]0.0196751303463845[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.9025427115651[/C][C]0.0191988709600782[/C][/ROW]
[ROW][C]Rectangular[/C][C]26.8699364518171[/C][C]0.0189689177648908[/C][/ROW]
[ROW][C]Triangular[/C][C]23.185927978726[/C][C]0.0194843188521844[/C][/ROW]
[ROW][C]Biweight[/C][C]22.9025427115651[/C][C]0.0193710306536086[/C][/ROW]
[ROW][C]Cosine[/C][C]22.9025427115651[/C][C]0.019422531203197[/C][/ROW]
[ROW][C]Optcosine[/C][C]23.185927978726[/C][C]0.0192640613854086[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190526&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190526&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
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular26.86993645181710.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular27.15332171897790.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.9025427115651 & 0.0196751303463845 \tabularnewline
Epanechnikov & 22.9025427115651 & 0.0191988709600782 \tabularnewline
Rectangular & 27.1533217189779 & 0.0189689177648908 \tabularnewline
Triangular & 23.185927978726 & 0.0194843188521844 \tabularnewline
Biweight & 22.9025427115651 & 0.0193710306536086 \tabularnewline
Cosine & 22.9025427115651 & 0.019422531203197 \tabularnewline
Optcosine & 23.185927978726 & 0.0192640613854086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190526&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]22.9025427115651[/C][C]0.0196751303463845[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.9025427115651[/C][C]0.0191988709600782[/C][/ROW]
[ROW][C]Rectangular[/C][C]27.1533217189779[/C][C]0.0189689177648908[/C][/ROW]
[ROW][C]Triangular[/C][C]23.185927978726[/C][C]0.0194843188521844[/C][/ROW]
[ROW][C]Biweight[/C][C]22.9025427115651[/C][C]0.0193710306536086[/C][/ROW]
[ROW][C]Cosine[/C][C]22.9025427115651[/C][C]0.019422531203197[/C][/ROW]
[ROW][C]Optcosine[/C][C]23.185927978726[/C][C]0.0192640613854086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190526&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190526&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
Gaussian22.90254271156510.0196751303463845
Epanechnikov22.90254271156510.0191988709600782
Rectangular27.15332171897790.0189689177648908
Triangular23.1859279787260.0194843188521844
Biweight22.90254271156510.0193710306536086
Cosine22.90254271156510.019422531203197
Optcosine23.1859279787260.0192640613854086


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')
}