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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 computationWed, 20 May 2015 11:10:45 +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/2015/May/20/t14321168782xc4gw1gnzkx5in.htm/, Retrieved Mon, 29 Apr 2024 03:16:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279151, Retrieved Mon, 29 Apr 2024 03:16:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136

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] [consumentenprijze...] [2015-05-20 10:10:45] [0793dda36b6d92f80d1980fc1d00d6bd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
98,68
99,06
99,84
100,3
100,38
100,02
99,83
100,36
100,74
100,49
100,33
99,96
100,08
100,54
101,63
102,12
102,19
101,77
101,29
101,47
102,07
102,11
102,26
101,83
102,11
102,8
103,82
104,2
104,57
104,38
104,54
104,74
105,19
104,95
104,57
103,81
104,08
104,81
105,86
106,1
106,24
105,87
104,74
105,03
105,59
105,69
105,58
104,96
104,93
105,68
106,93
107,29
107,25
106,74
106,44
106,6
107,26
107,35
107,22
106,99
106,87
107,68
108,9
109,48
109,57
109,03
109,58
109,76
110,15
110,2
109,86
109,58
109,52
110,35
111,61
112,06
111,9
111,36
112,09
112,24
112,7
113,36
112,9
112,74
112,77
113,66
114,87
114,97
115
114,57
115,54
115,39
115,46
115,13
114,56
114,62

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'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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279151&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279151&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279151&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth7
#Observations96

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 7 \tabularnewline
#Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279151&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]7[/C][/ROW]
[ROW][C]#Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279151&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279151&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
Bandwidth7
#Observations96






Maximum Density Values
Kernelx-valuemax. density
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular103.9423874755380.0412393049421161
Triangular105.9005479452050.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 106.361291585127 & 0.0463921336917959 \tabularnewline
Epanechnikov & 106.706849315069 & 0.0434798111477504 \tabularnewline
Rectangular & 103.942387475538 & 0.0412393049421161 \tabularnewline
Triangular & 105.900547945205 & 0.0448497427857808 \tabularnewline
Biweight & 106.591663405088 & 0.0443699998424339 \tabularnewline
Cosine & 106.591663405088 & 0.0446708513735581 \tabularnewline
Optcosine & 106.706849315069 & 0.0437374749270303 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279151&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]106.361291585127[/C][C]0.0463921336917959[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]106.706849315069[/C][C]0.0434798111477504[/C][/ROW]
[ROW][C]Rectangular[/C][C]103.942387475538[/C][C]0.0412393049421161[/C][/ROW]
[ROW][C]Triangular[/C][C]105.900547945205[/C][C]0.0448497427857808[/C][/ROW]
[ROW][C]Biweight[/C][C]106.591663405088[/C][C]0.0443699998424339[/C][/ROW]
[ROW][C]Cosine[/C][C]106.591663405088[/C][C]0.0446708513735581[/C][/ROW]
[ROW][C]Optcosine[/C][C]106.706849315069[/C][C]0.0437374749270303[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279151&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279151&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
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular103.9423874755380.0412393049421161
Triangular105.9005479452050.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303






Maximum Density Values
Kernelx-valuemax. density
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular104.2879452054790.0412393049421161
Triangular106.0157338551860.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 106.361291585127 & 0.0463921336917959 \tabularnewline
Epanechnikov & 106.706849315069 & 0.0434798111477504 \tabularnewline
Rectangular & 104.287945205479 & 0.0412393049421161 \tabularnewline
Triangular & 106.015733855186 & 0.0448497427857808 \tabularnewline
Biweight & 106.591663405088 & 0.0443699998424339 \tabularnewline
Cosine & 106.591663405088 & 0.0446708513735581 \tabularnewline
Optcosine & 106.706849315069 & 0.0437374749270303 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279151&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]106.361291585127[/C][C]0.0463921336917959[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]106.706849315069[/C][C]0.0434798111477504[/C][/ROW]
[ROW][C]Rectangular[/C][C]104.287945205479[/C][C]0.0412393049421161[/C][/ROW]
[ROW][C]Triangular[/C][C]106.015733855186[/C][C]0.0448497427857808[/C][/ROW]
[ROW][C]Biweight[/C][C]106.591663405088[/C][C]0.0443699998424339[/C][/ROW]
[ROW][C]Cosine[/C][C]106.591663405088[/C][C]0.0446708513735581[/C][/ROW]
[ROW][C]Optcosine[/C][C]106.706849315069[/C][C]0.0437374749270303[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279151&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279151&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
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular104.2879452054790.0412393049421161
Triangular106.0157338551860.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303






Maximum Density Values
Kernelx-valuemax. density
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular104.403131115460.0412393049421161
Triangular105.9005479452050.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 106.361291585127 & 0.0463921336917959 \tabularnewline
Epanechnikov & 106.706849315069 & 0.0434798111477504 \tabularnewline
Rectangular & 104.40313111546 & 0.0412393049421161 \tabularnewline
Triangular & 105.900547945205 & 0.0448497427857808 \tabularnewline
Biweight & 106.591663405088 & 0.0443699998424339 \tabularnewline
Cosine & 106.591663405088 & 0.0446708513735581 \tabularnewline
Optcosine & 106.706849315069 & 0.0437374749270303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279151&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]106.361291585127[/C][C]0.0463921336917959[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]106.706849315069[/C][C]0.0434798111477504[/C][/ROW]
[ROW][C]Rectangular[/C][C]104.40313111546[/C][C]0.0412393049421161[/C][/ROW]
[ROW][C]Triangular[/C][C]105.900547945205[/C][C]0.0448497427857808[/C][/ROW]
[ROW][C]Biweight[/C][C]106.591663405088[/C][C]0.0443699998424339[/C][/ROW]
[ROW][C]Cosine[/C][C]106.591663405088[/C][C]0.0446708513735581[/C][/ROW]
[ROW][C]Optcosine[/C][C]106.706849315069[/C][C]0.0437374749270303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279151&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279151&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
Gaussian106.3612915851270.0463921336917959
Epanechnikov106.7068493150690.0434798111477504
Rectangular104.403131115460.0412393049421161
Triangular105.9005479452050.0448497427857808
Biweight106.5916634050880.0443699998424339
Cosine106.5916634050880.0446708513735581
Optcosine106.7068493150690.0437374749270303


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 7 ; 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')
}