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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, 29 Nov 2017 11:13:23 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/29/t1511950471sja5chjb7v8h2vd.htm/, Retrieved Sat, 18 May 2024 17:57:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308283, Retrieved Sat, 18 May 2024 17:57:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSection C - Manufacturing
Estimated Impact91

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 Es...] [2017-11-29 10:13:23] [e32c8f3a6c40fa6b5d041988204898ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
58,4
64,8
73,8
65
73
71,1
58,2
64
75
74,9
75
68,3
72,5
72,4
79,6
70,7
76,4
79,7
64,2
67,9
74,1
78,5
73,4
65,4
69,9
69,6
76,8
75,6
74
76
68,1
65,5
76,9
81,7
73,6
68,7
73,3
71,5
78,3
76,5
71,8
77,6
70
64
81,3
82,5
73,1
78,1
70,7
74,9
88
81,3
75,7
89,8
74,6
74,9
90
88,1
84,9
87,7
80,5
79
89,9
86,3
81,1
92,4
71,8
76,1
92,5
87
89,5
88,7
83,8
84,9
99
84,6
92,7
97,6
78
81,9
96,5
99,9
96,2
90,5
91,4
89,7
102,7
91,5
96,2
104,5
90,3
90,3
100,4
111,3
101,3
94,4
100,4
102
104,3
108,8
101,3
108,9
98,5
88,8
111,8
109,6
92,5
94,5
80,8
83,7
94,2
86,2
89
94,7
81,9
80,2
96,5
95,6
91,9
89,9
86,3
94
108
96,3
94,6
111,7
92
91,9
109,2
106,8
105,8
103,6
97,6
102,8
124,8
103,9
112,2
108,5
92,4
101,1
114,9
106,4
104
101,6
99,4
102,3
121,3
99,3
102,9
111,4
98,5
98,5
108,5
112,1
105,3
95,2
98,2
96,6
109,6
108
106,7
111,5
104,5
94,3
109,6
116,4
106,5
100,5
101,7
104,1
112,3
111,2
108,2
115,1
102,3
93,6
120,6
118,4
106,6
105,3
101,5
100,1
119,5
111,2
103,7
117,8
101,7
97,4
120
117
110,6
105,3
100,9
108,1
119,3
113
108,6
123,3
101,4
103,5
119,4
113,1
112
115,8

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308283&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308283&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308283&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center






Properties of Density Trace
Bandwidth4.85782485134168
#Observations204

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 4.85782485134168 \tabularnewline
#Observations & 204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308283&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]4.85782485134168[/C][/ROW]
[ROW][C]#Observations[/C][C]204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308283&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308283&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
Bandwidth4.85782485134168
#Observations204






Maximum Density Values
Kernelx-valuemax. density
Gaussian101.7117587600560.0228380129638775
Epanechnikov102.273873921160.0226765496884402
Rectangular104.147591124840.0229448371323106
Triangular101.5243870396880.022987886994793
Biweight101.7117587600560.0227140908208633
Cosine101.5243870396880.0227446262952687
Optcosine102.273873921160.0227176052581201

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 101.711758760056 & 0.0228380129638775 \tabularnewline
Epanechnikov & 102.27387392116 & 0.0226765496884402 \tabularnewline
Rectangular & 104.14759112484 & 0.0229448371323106 \tabularnewline
Triangular & 101.524387039688 & 0.022987886994793 \tabularnewline
Biweight & 101.711758760056 & 0.0227140908208633 \tabularnewline
Cosine & 101.524387039688 & 0.0227446262952687 \tabularnewline
Optcosine & 102.27387392116 & 0.0227176052581201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308283&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]101.711758760056[/C][C]0.0228380129638775[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]102.27387392116[/C][C]0.0226765496884402[/C][/ROW]
[ROW][C]Rectangular[/C][C]104.14759112484[/C][C]0.0229448371323106[/C][/ROW]
[ROW][C]Triangular[/C][C]101.524387039688[/C][C]0.022987886994793[/C][/ROW]
[ROW][C]Biweight[/C][C]101.711758760056[/C][C]0.0227140908208633[/C][/ROW]
[ROW][C]Cosine[/C][C]101.524387039688[/C][C]0.0227446262952687[/C][/ROW]
[ROW][C]Optcosine[/C][C]102.27387392116[/C][C]0.0227176052581201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308283&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308283&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
Gaussian101.7117587600560.0228380129638775
Epanechnikov102.273873921160.0226765496884402
Rectangular104.147591124840.0229448371323106
Triangular101.5243870396880.022987886994793
Biweight101.7117587600560.0227140908208633
Cosine101.5243870396880.0227446262952687
Optcosine102.273873921160.0227176052581201






Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown

\begin{tabular}{lllllllll}
\hline
Kernel Density Values \tabularnewline
x-value & Gaussian & Epanechnikov & Rectangular & Triangular & Biweight & Cosine & Optcosine \tabularnewline
Kernel Density Values are not shown \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308283&T=3

[TABLE]
[ROW][C]Kernel Density Values[/C][/ROW]
[ROW][C]x-value[/C][C]Gaussian[/C][C]Epanechnikov[/C][C]Rectangular[/C][C]Triangular[/C][C]Biweight[/C][C]Cosine[/C][C]Optcosine[/C][/ROW]
[ROW][C]Kernel Density Values are not shown[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308283&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308283&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:

Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = grey ; par2 = no ;
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')
ab<-table.start()
ab<-table.row.start(ab)
ab<-table.element(ab,'Properties of Density Trace',2,TRUE)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'Bandwidth',header=TRUE)
ab<-table.element(ab,mydensity1$bw)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'#Observations',header=TRUE)
ab<-table.element(ab,mydensity1$n)
ab<-table.row.end(ab)
ab<-table.end(ab)
a <- ab
table.save(ab,file='mytable123.tab')
b<-table.start()
b<-table.row.start(b)
b<-table.element(b,'Maximum Density Values',3,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Kernel',1,TRUE)
b<-table.element(b,'x-value',1,TRUE)
b<-table.element(b,'max. density',1,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Gaussian',1,TRUE)
b<-table.element(b,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
b<-table.element(b,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Epanechnikov',1,TRUE)
b<-table.element(b,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
b<-table.element(b,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Rectangular',1,TRUE)
b<-table.element(b,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
b<-table.element(b,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Triangular',1,TRUE)
b<-table.element(b,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
b<-table.element(b,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Biweight',1,TRUE)
b<-table.element(b,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
b<-table.element(b,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Cosine',1,TRUE)
b<-table.element(b,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
b<-table.element(b,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Optcosine',1,TRUE)
b<-table.element(b,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
b<-table.element(b,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
b<-table.row.end(b)
b<-table.end(b)
a <- b[1]
table.save(b,file='mytable2a.tab')
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)
if (par2=='yes') {
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)
}
} else {
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values are not shown',8)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')