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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationMon, 02 Feb 2015 10:42:13 +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/2015/Feb/02/t1422873795pmudijwark93xoe.htm/, Retrieved Fri, 31 May 2024 12:49:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=276427, Retrieved Fri, 31 May 2024 12:49:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Prijsindex gronds...] [2015-01-26 10:30:11] [133f5cfcb309decd018975e303cedd6d]
- RMP     [Kernel Density Estimation] [] [2015-02-02 10:42:13] [9d11e60232d68c92754922ab1f7d0739] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
78.7
75.7
77.1
86.1
86.8
86.3
91.5
90.7
78.2
73
73.7
77.3
67.5
72.7
76.6
82.4
82.3
86.3
93
88.8
96.9
103.9
115.7
112.8
114.7
118
129.3
137
156
166.2
167.8
144.3
126
90.4
67.5
52.4
54.6
52.9
59.1
63.3
73.8
87.6
81.8
90.7
86.3
93.6
98
94.3
97.6
94.2
100.2
106.7
95.7
94.6
94.7
96.2
96.3
103.3
106.8
113.7
117.4
123.6
137.6
147.4
137.2
133.8
136.7
127.3
128.7
127
133.7
132
135.1
142.6
149.3
143.5
131.4
114.7
122.3
133.4
134.6
130.9
127.9
128
133.3
136.3
129.5
124.6
125.5
126.2
133.3
137
137.8
133.5
129.9
133.3

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276427&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276427&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276427&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'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth9.85733205899717
#Observations96

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 9.85733205899717 \tabularnewline
#Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276427&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]9.85733205899717[/C][/ROW]
[ROW][C]#Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276427&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276427&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
Bandwidth9.85733205899717
#Observations96






Maximum Density Values
Kernelx-valuemax. density
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.0326019541760.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 131.106762289178 & 0.0143271978226093 \tabularnewline
Epanechnikov & 130.423615548067 & 0.0134347878051677 \tabularnewline
Rectangular & 128.032601954176 & 0.0131173834119995 \tabularnewline
Triangular & 131.448335659734 & 0.0138935442619122 \tabularnewline
Biweight & 130.423615548067 & 0.0136610715218054 \tabularnewline
Cosine & 130.765188918622 & 0.0137586724074116 \tabularnewline
Optcosine & 130.423615548067 & 0.0135004135588174 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276427&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]131.106762289178[/C][C]0.0143271978226093[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]130.423615548067[/C][C]0.0134347878051677[/C][/ROW]
[ROW][C]Rectangular[/C][C]128.032601954176[/C][C]0.0131173834119995[/C][/ROW]
[ROW][C]Triangular[/C][C]131.448335659734[/C][C]0.0138935442619122[/C][/ROW]
[ROW][C]Biweight[/C][C]130.423615548067[/C][C]0.0136610715218054[/C][/ROW]
[ROW][C]Cosine[/C][C]130.765188918622[/C][C]0.0137586724074116[/C][/ROW]
[ROW][C]Optcosine[/C][C]130.423615548067[/C][C]0.0135004135588174[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276427&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276427&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
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.0326019541760.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174






Maximum Density Values
Kernelx-valuemax. density
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.3741753247320.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 131.106762289178 & 0.0143271978226093 \tabularnewline
Epanechnikov & 130.423615548067 & 0.0134347878051677 \tabularnewline
Rectangular & 128.374175324732 & 0.0131173834119995 \tabularnewline
Triangular & 131.448335659734 & 0.0138935442619122 \tabularnewline
Biweight & 130.423615548067 & 0.0136610715218054 \tabularnewline
Cosine & 130.765188918622 & 0.0137586724074116 \tabularnewline
Optcosine & 130.423615548067 & 0.0135004135588174 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276427&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]131.106762289178[/C][C]0.0143271978226093[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]130.423615548067[/C][C]0.0134347878051677[/C][/ROW]
[ROW][C]Rectangular[/C][C]128.374175324732[/C][C]0.0131173834119995[/C][/ROW]
[ROW][C]Triangular[/C][C]131.448335659734[/C][C]0.0138935442619122[/C][/ROW]
[ROW][C]Biweight[/C][C]130.423615548067[/C][C]0.0136610715218054[/C][/ROW]
[ROW][C]Cosine[/C][C]130.765188918622[/C][C]0.0137586724074116[/C][/ROW]
[ROW][C]Optcosine[/C][C]130.423615548067[/C][C]0.0135004135588174[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276427&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276427&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
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.3741753247320.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174






Maximum Density Values
Kernelx-valuemax. density
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.7157486952880.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 131.106762289178 & 0.0143271978226093 \tabularnewline
Epanechnikov & 130.423615548067 & 0.0134347878051677 \tabularnewline
Rectangular & 128.715748695288 & 0.0131173834119995 \tabularnewline
Triangular & 131.448335659734 & 0.0138935442619122 \tabularnewline
Biweight & 130.423615548067 & 0.0136610715218054 \tabularnewline
Cosine & 130.765188918622 & 0.0137586724074116 \tabularnewline
Optcosine & 130.423615548067 & 0.0135004135588174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276427&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]131.106762289178[/C][C]0.0143271978226093[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]130.423615548067[/C][C]0.0134347878051677[/C][/ROW]
[ROW][C]Rectangular[/C][C]128.715748695288[/C][C]0.0131173834119995[/C][/ROW]
[ROW][C]Triangular[/C][C]131.448335659734[/C][C]0.0138935442619122[/C][/ROW]
[ROW][C]Biweight[/C][C]130.423615548067[/C][C]0.0136610715218054[/C][/ROW]
[ROW][C]Cosine[/C][C]130.765188918622[/C][C]0.0137586724074116[/C][/ROW]
[ROW][C]Optcosine[/C][C]130.423615548067[/C][C]0.0135004135588174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276427&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276427&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
Gaussian131.1067622891780.0143271978226093
Epanechnikov130.4236155480670.0134347878051677
Rectangular128.7157486952880.0131173834119995
Triangular131.4483356597340.0138935442619122
Biweight130.4236155480670.0136610715218054
Cosine130.7651889186220.0137586724074116
Optcosine130.4236155480670.0135004135588174


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = grey ; par3 = TRUE ; par4 = Interval/Ratio ;
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')
}