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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 computationThu, 26 Sep 2013 09:10:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Sep/26/t1380201038snx4cbb3g15m4vj.htm/, Retrieved Mon, 29 Apr 2024 15:56:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212101, Retrieved Mon, 29 Apr 2024 15:56:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

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] [] [2013-09-26 13:10:29] [62756545679af31f2a2b14ff700a18b9] [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

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=212101&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=212101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212101&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
Bandwidth10.2332463550852
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 10.2332463550852 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212101&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]10.2332463550852[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212101&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
Bandwidth10.2332463550852
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.16777215871640.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 89.8597466328084 & 0.0137537012120826 \tabularnewline
Epanechnikov & 87.7838232105324 & 0.0133691221642476 \tabularnewline
Rectangular & 89.1677721587164 & 0.0137689403404436 \tabularnewline
Triangular & 90.5517211069005 & 0.0134763576990461 \tabularnewline
Biweight & 88.4757976846244 & 0.0134278252179298 \tabularnewline
Cosine & 89.1677721587164 & 0.0134728526218096 \tabularnewline
Optcosine & 88.1298104475784 & 0.0133737034679239 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212101&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]89.8597466328084[/C][C]0.0137537012120826[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.7838232105324[/C][C]0.0133691221642476[/C][/ROW]
[ROW][C]Rectangular[/C][C]89.1677721587164[/C][C]0.0137689403404436[/C][/ROW]
[ROW][C]Triangular[/C][C]90.5517211069005[/C][C]0.0134763576990461[/C][/ROW]
[ROW][C]Biweight[/C][C]88.4757976846244[/C][C]0.0134278252179298[/C][/ROW]
[ROW][C]Cosine[/C][C]89.1677721587164[/C][C]0.0134728526218096[/C][/ROW]
[ROW][C]Optcosine[/C][C]88.1298104475784[/C][C]0.0133737034679239[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212101&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212101&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
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.16777215871640.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239






Maximum Density Values
Kernelx-valuemax. density
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.51375939576240.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 89.8597466328084 & 0.0137537012120826 \tabularnewline
Epanechnikov & 87.7838232105324 & 0.0133691221642476 \tabularnewline
Rectangular & 89.5137593957624 & 0.0137689403404436 \tabularnewline
Triangular & 90.5517211069005 & 0.0134763576990461 \tabularnewline
Biweight & 88.4757976846244 & 0.0134278252179298 \tabularnewline
Cosine & 89.1677721587164 & 0.0134728526218096 \tabularnewline
Optcosine & 88.1298104475784 & 0.0133737034679239 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212101&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]89.8597466328084[/C][C]0.0137537012120826[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.7838232105324[/C][C]0.0133691221642476[/C][/ROW]
[ROW][C]Rectangular[/C][C]89.5137593957624[/C][C]0.0137689403404436[/C][/ROW]
[ROW][C]Triangular[/C][C]90.5517211069005[/C][C]0.0134763576990461[/C][/ROW]
[ROW][C]Biweight[/C][C]88.4757976846244[/C][C]0.0134278252179298[/C][/ROW]
[ROW][C]Cosine[/C][C]89.1677721587164[/C][C]0.0134728526218096[/C][/ROW]
[ROW][C]Optcosine[/C][C]88.1298104475784[/C][C]0.0133737034679239[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212101&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212101&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
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.51375939576240.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239






Maximum Density Values
Kernelx-valuemax. density
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.85974663280840.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 89.8597466328084 & 0.0137537012120826 \tabularnewline
Epanechnikov & 87.7838232105324 & 0.0133691221642476 \tabularnewline
Rectangular & 89.8597466328084 & 0.0137689403404436 \tabularnewline
Triangular & 90.5517211069005 & 0.0134763576990461 \tabularnewline
Biweight & 88.4757976846244 & 0.0134278252179298 \tabularnewline
Cosine & 89.1677721587164 & 0.0134728526218096 \tabularnewline
Optcosine & 88.1298104475784 & 0.0133737034679239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212101&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]89.8597466328084[/C][C]0.0137537012120826[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.7838232105324[/C][C]0.0133691221642476[/C][/ROW]
[ROW][C]Rectangular[/C][C]89.8597466328084[/C][C]0.0137689403404436[/C][/ROW]
[ROW][C]Triangular[/C][C]90.5517211069005[/C][C]0.0134763576990461[/C][/ROW]
[ROW][C]Biweight[/C][C]88.4757976846244[/C][C]0.0134278252179298[/C][/ROW]
[ROW][C]Cosine[/C][C]89.1677721587164[/C][C]0.0134728526218096[/C][/ROW]
[ROW][C]Optcosine[/C][C]88.1298104475784[/C][C]0.0133737034679239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212101&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212101&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
Gaussian89.85974663280840.0137537012120826
Epanechnikov87.78382321053240.0133691221642476
Rectangular89.85974663280840.0137689403404436
Triangular90.55172110690050.0134763576990461
Biweight88.47579768462440.0134278252179298
Cosine89.16777215871640.0134728526218096
Optcosine88.12981044757840.0133737034679239


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')
}