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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, 18 May 2015 16:37:59 +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/18/t143196351054jep33ayqqutlk.htm/, Retrieved Thu, 02 May 2024 07:11:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279110, Retrieved Thu, 02 May 2024 07:11:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [dichtheidsgrafiek] [2015-05-18 15:37:59] [b43493158838656c32486372ca9c54cf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.8
100.66
101.44
102.17
102.75
104.28
104.96
105.16
105.29
105.15
105.23
104.45
104.6
105.1
105.94
106.2
106.89
107.57
107.42
107.2
107.08
107.17
107.23
106.61
106.97
108.23
109.8
111.93
113.51
115.27
115.58
115.55
115.44
114.93
115.09
113.78
114.51
114.85
116.12
115.47
115.93
116.6
116.98
117.37
117.48
117.18
117.03
114.95
115.64
116.02
116.07
114.5
114.36
116
116.16
116.42
116.78
115.74
115.44
113.52
113.37
114.35
114.11
113.47
114.33
115.76
116.2
116.48
116.53
116.45
116.23
114.46
115.08
115.57
116.17
115.21
114.97
114.24
114.16
117.2
117.71
117.14
116.67
114.71
115.92
117.74
118.38
118.59
119.66
121.2
121.4
122.66
122.95
122.9
123.29
122.02

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 Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&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 Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth1.98415754455371
#Observations96

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.98415754455371 \tabularnewline
#Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.98415754455371[/C][/ROW]
[ROW][C]#Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&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
Bandwidth1.98415754455371
#Observations96






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.4016906360270.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.658276941427 & 0.106781920111549 \tabularnewline
Epanechnikov & 115.658276941427 & 0.0982803002020605 \tabularnewline
Rectangular & 116.401690636027 & 0.092446787946491 \tabularnewline
Triangular & 115.658276941427 & 0.10275659962917 \tabularnewline
Biweight & 115.658276941427 & 0.100850394758121 \tabularnewline
Cosine & 115.658276941427 & 0.101755791434303 \tabularnewline
Optcosine & 115.658276941427 & 0.0990979411125308 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&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]115.658276941427[/C][C]0.106781920111549[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.658276941427[/C][C]0.0982803002020605[/C][/ROW]
[ROW][C]Rectangular[/C][C]116.401690636027[/C][C]0.092446787946491[/C][/ROW]
[ROW][C]Triangular[/C][C]115.658276941427[/C][C]0.10275659962917[/C][/ROW]
[ROW][C]Biweight[/C][C]115.658276941427[/C][C]0.100850394758121[/C][/ROW]
[ROW][C]Cosine[/C][C]115.658276941427[/C][C]0.101755791434303[/C][/ROW]
[ROW][C]Optcosine[/C][C]115.658276941427[/C][C]0.0990979411125308[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&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
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.4016906360270.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.4692736991720.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.658276941427 & 0.106781920111549 \tabularnewline
Epanechnikov & 115.658276941427 & 0.0982803002020605 \tabularnewline
Rectangular & 116.469273699172 & 0.092446787946491 \tabularnewline
Triangular & 115.658276941427 & 0.10275659962917 \tabularnewline
Biweight & 115.658276941427 & 0.100850394758121 \tabularnewline
Cosine & 115.658276941427 & 0.101755791434303 \tabularnewline
Optcosine & 115.658276941427 & 0.0990979411125308 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&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]115.658276941427[/C][C]0.106781920111549[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.658276941427[/C][C]0.0982803002020605[/C][/ROW]
[ROW][C]Rectangular[/C][C]116.469273699172[/C][C]0.092446787946491[/C][/ROW]
[ROW][C]Triangular[/C][C]115.658276941427[/C][C]0.10275659962917[/C][/ROW]
[ROW][C]Biweight[/C][C]115.658276941427[/C][C]0.100850394758121[/C][/ROW]
[ROW][C]Cosine[/C][C]115.658276941427[/C][C]0.101755791434303[/C][/ROW]
[ROW][C]Optcosine[/C][C]115.658276941427[/C][C]0.0990979411125308[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&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
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.4692736991720.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.5368567623180.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.658276941427 & 0.106781920111549 \tabularnewline
Epanechnikov & 115.658276941427 & 0.0982803002020605 \tabularnewline
Rectangular & 116.536856762318 & 0.092446787946491 \tabularnewline
Triangular & 115.658276941427 & 0.10275659962917 \tabularnewline
Biweight & 115.658276941427 & 0.100850394758121 \tabularnewline
Cosine & 115.658276941427 & 0.101755791434303 \tabularnewline
Optcosine & 115.658276941427 & 0.0990979411125308 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&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]115.658276941427[/C][C]0.106781920111549[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.658276941427[/C][C]0.0982803002020605[/C][/ROW]
[ROW][C]Rectangular[/C][C]116.536856762318[/C][C]0.092446787946491[/C][/ROW]
[ROW][C]Triangular[/C][C]115.658276941427[/C][C]0.10275659962917[/C][/ROW]
[ROW][C]Biweight[/C][C]115.658276941427[/C][C]0.100850394758121[/C][/ROW]
[ROW][C]Cosine[/C][C]115.658276941427[/C][C]0.101755791434303[/C][/ROW]
[ROW][C]Optcosine[/C][C]115.658276941427[/C][C]0.0990979411125308[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&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
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.5368567623180.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.6044398254630.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.658276941427 & 0.106781920111549 \tabularnewline
Epanechnikov & 115.658276941427 & 0.0982803002020605 \tabularnewline
Rectangular & 116.604439825463 & 0.092446787946491 \tabularnewline
Triangular & 115.658276941427 & 0.10275659962917 \tabularnewline
Biweight & 115.658276941427 & 0.100850394758121 \tabularnewline
Cosine & 115.658276941427 & 0.101755791434303 \tabularnewline
Optcosine & 115.658276941427 & 0.0990979411125308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279110&T=5

[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]115.658276941427[/C][C]0.106781920111549[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.658276941427[/C][C]0.0982803002020605[/C][/ROW]
[ROW][C]Rectangular[/C][C]116.604439825463[/C][C]0.092446787946491[/C][/ROW]
[ROW][C]Triangular[/C][C]115.658276941427[/C][C]0.10275659962917[/C][/ROW]
[ROW][C]Biweight[/C][C]115.658276941427[/C][C]0.100850394758121[/C][/ROW]
[ROW][C]Cosine[/C][C]115.658276941427[/C][C]0.101755791434303[/C][/ROW]
[ROW][C]Optcosine[/C][C]115.658276941427[/C][C]0.0990979411125308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279110&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279110&T=5

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
Gaussian115.6582769414270.106781920111549
Epanechnikov115.6582769414270.0982803002020605
Rectangular116.6044398254630.092446787946491
Triangular115.6582769414270.10275659962917
Biweight115.6582769414270.100850394758121
Cosine115.6582769414270.101755791434303
Optcosine115.6582769414270.0990979411125308


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')
}