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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 15:13:46 +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/t14186564351ut8phrpuw593cl.htm/, Retrieved Thu, 16 May 2024 08:11:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268611, Retrieved Thu, 16 May 2024 08:11:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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 IM] [2014-12-15 15:13:46] [9636d26fd774798d33054b538c301d75] [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
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

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268611&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268611&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268611&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth2.81713628069321
#Observations286

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.81713628069321 \tabularnewline
#Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268611&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.81713628069321[/C][/ROW]
[ROW][C]#Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268611&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268611&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
Bandwidth2.81713628069321
#Observations286






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.57223205520440.0428961531214178
Epanechnikov54.07068303965150.0432916495899542
Rectangular54.40298369594950.0455029138265308
Triangular53.07378107075720.0425959165813978
Biweight53.73838238335340.043111175914534
Cosine53.73838238335340.0430687717574739
Optcosine54.07068303965150.0432175826975874

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.5722320552044 & 0.0428961531214178 \tabularnewline
Epanechnikov & 54.0706830396515 & 0.0432916495899542 \tabularnewline
Rectangular & 54.4029836959495 & 0.0455029138265308 \tabularnewline
Triangular & 53.0737810707572 & 0.0425959165813978 \tabularnewline
Biweight & 53.7383823833534 & 0.043111175914534 \tabularnewline
Cosine & 53.7383823833534 & 0.0430687717574739 \tabularnewline
Optcosine & 54.0706830396515 & 0.0432175826975874 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268611&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]53.5722320552044[/C][C]0.0428961531214178[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0706830396515[/C][C]0.0432916495899542[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.4029836959495[/C][C]0.0455029138265308[/C][/ROW]
[ROW][C]Triangular[/C][C]53.0737810707572[/C][C]0.0425959165813978[/C][/ROW]
[ROW][C]Biweight[/C][C]53.7383823833534[/C][C]0.043111175914534[/C][/ROW]
[ROW][C]Cosine[/C][C]53.7383823833534[/C][C]0.0430687717574739[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.0706830396515[/C][C]0.0432175826975874[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268611&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268611&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
Gaussian53.57223205520440.0428961531214178
Epanechnikov54.07068303965150.0432916495899542
Rectangular54.40298369594950.0455029138265308
Triangular53.07378107075720.0425959165813978
Biweight53.73838238335340.043111175914534
Cosine53.73838238335340.0430687717574739
Optcosine54.07068303965150.0432175826975874






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.57223205520440.0428961531214178
Epanechnikov54.07068303965150.0432916495899542
Rectangular54.56913402409860.0455029138265308
Triangular53.07378107075720.0425959165813978
Biweight53.73838238335340.043111175914534
Cosine53.73838238335340.0430687717574739
Optcosine54.07068303965150.0432175826975874

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.5722320552044 & 0.0428961531214178 \tabularnewline
Epanechnikov & 54.0706830396515 & 0.0432916495899542 \tabularnewline
Rectangular & 54.5691340240986 & 0.0455029138265308 \tabularnewline
Triangular & 53.0737810707572 & 0.0425959165813978 \tabularnewline
Biweight & 53.7383823833534 & 0.043111175914534 \tabularnewline
Cosine & 53.7383823833534 & 0.0430687717574739 \tabularnewline
Optcosine & 54.0706830396515 & 0.0432175826975874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268611&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]53.5722320552044[/C][C]0.0428961531214178[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]54.0706830396515[/C][C]0.0432916495899542[/C][/ROW]
[ROW][C]Rectangular[/C][C]54.5691340240986[/C][C]0.0455029138265308[/C][/ROW]
[ROW][C]Triangular[/C][C]53.0737810707572[/C][C]0.0425959165813978[/C][/ROW]
[ROW][C]Biweight[/C][C]53.7383823833534[/C][C]0.043111175914534[/C][/ROW]
[ROW][C]Cosine[/C][C]53.7383823833534[/C][C]0.0430687717574739[/C][/ROW]
[ROW][C]Optcosine[/C][C]54.0706830396515[/C][C]0.0432175826975874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268611&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268611&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
Gaussian53.57223205520440.0428961531214178
Epanechnikov54.07068303965150.0432916495899542
Rectangular54.56913402409860.0455029138265308
Triangular53.07378107075720.0425959165813978
Biweight53.73838238335340.043111175914534
Cosine53.73838238335340.0430687717574739
Optcosine54.07068303965150.0432175826975874


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')
}