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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 computationTue, 12 Feb 2013 17:31:29 -0500
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/Feb/12/t1360708412dz0vc2lw7d3s7so.htm/, Retrieved Sun, 28 Apr 2024 22:31:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=206469, Retrieved Sun, 28 Apr 2024 22:31:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [] [2013-02-12 22:31:29] [f5344c9d857de7b42142f71fd8a100cb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
530,3
527,76
521,41
1601,93
1577,49
1551,43
1551,43
1516,88
1485,95
1438,22
1385,06
1329,49
1329,49
1276,16
1242,34
1181,59
1160,21
1135,18
1135,18
1084,96
1077,35
1061,13
1029,98
1013,08
1013,08
996,04
975,02
951,89
944,4
932,47
932,47
920,44
900,18
886,9
867,74
859,03
859,03
844,99
834,82
825,62
816,92
813,21
813,21
811,03
804,16
788,62
778,76
765,91
765,91
753,85
742,22
732,11
729,94
731,22
731,22
729,11
726,94
720,52
709,36
703,21
703,21
695,88
681,63
672,1
665,49
658,93
658,93
656
650,66
645,93
638,74
634,67

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&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]5 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=206469&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth97.041720120375
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 97.041720120375 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]97.041720120375[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206469&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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
Bandwidth97.041720120375
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular789.9648693144660.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 754.171379044515 & 0.0018308121967368 \tabularnewline
Epanechnikov & 776.949054670848 & 0.0017805043023184 \tabularnewline
Rectangular & 789.964869314466 & 0.00185922053832057 \tabularnewline
Triangular & 744.409518061802 & 0.00178414378749848 \tabularnewline
Biweight & 767.187193688134 & 0.00178868959247452 \tabularnewline
Cosine & 763.933240027229 & 0.0017948312434571 \tabularnewline
Optcosine & 776.949054670848 & 0.00178030690124362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&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]754.171379044515[/C][C]0.0018308121967368[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]776.949054670848[/C][C]0.0017805043023184[/C][/ROW]
[ROW][C]Rectangular[/C][C]789.964869314466[/C][C]0.00185922053832057[/C][/ROW]
[ROW][C]Triangular[/C][C]744.409518061802[/C][C]0.00178414378749848[/C][/ROW]
[ROW][C]Biweight[/C][C]767.187193688134[/C][C]0.00178868959247452[/C][/ROW]
[ROW][C]Cosine[/C][C]763.933240027229[/C][C]0.0017948312434571[/C][/ROW]
[ROW][C]Optcosine[/C][C]776.949054670848[/C][C]0.00178030690124362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206469&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular789.9648693144660.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362






Maximum Density Values
Kernelx-valuemax. density
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular793.2188229753710.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 754.171379044515 & 0.0018308121967368 \tabularnewline
Epanechnikov & 776.949054670848 & 0.0017805043023184 \tabularnewline
Rectangular & 793.218822975371 & 0.00185922053832057 \tabularnewline
Triangular & 744.409518061802 & 0.00178414378749848 \tabularnewline
Biweight & 767.187193688134 & 0.00178868959247452 \tabularnewline
Cosine & 763.933240027229 & 0.0017948312434571 \tabularnewline
Optcosine & 776.949054670848 & 0.00178030690124362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&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]754.171379044515[/C][C]0.0018308121967368[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]776.949054670848[/C][C]0.0017805043023184[/C][/ROW]
[ROW][C]Rectangular[/C][C]793.218822975371[/C][C]0.00185922053832057[/C][/ROW]
[ROW][C]Triangular[/C][C]744.409518061802[/C][C]0.00178414378749848[/C][/ROW]
[ROW][C]Biweight[/C][C]767.187193688134[/C][C]0.00178868959247452[/C][/ROW]
[ROW][C]Cosine[/C][C]763.933240027229[/C][C]0.0017948312434571[/C][/ROW]
[ROW][C]Optcosine[/C][C]776.949054670848[/C][C]0.00178030690124362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206469&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular793.2188229753710.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362






Maximum Density Values
Kernelx-valuemax. density
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular796.4727766362750.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 754.171379044515 & 0.0018308121967368 \tabularnewline
Epanechnikov & 776.949054670848 & 0.0017805043023184 \tabularnewline
Rectangular & 796.472776636275 & 0.00185922053832057 \tabularnewline
Triangular & 744.409518061802 & 0.00178414378749848 \tabularnewline
Biweight & 767.187193688134 & 0.00178868959247452 \tabularnewline
Cosine & 763.933240027229 & 0.0017948312434571 \tabularnewline
Optcosine & 776.949054670848 & 0.00178030690124362 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&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]754.171379044515[/C][C]0.0018308121967368[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]776.949054670848[/C][C]0.0017805043023184[/C][/ROW]
[ROW][C]Rectangular[/C][C]796.472776636275[/C][C]0.00185922053832057[/C][/ROW]
[ROW][C]Triangular[/C][C]744.409518061802[/C][C]0.00178414378749848[/C][/ROW]
[ROW][C]Biweight[/C][C]767.187193688134[/C][C]0.00178868959247452[/C][/ROW]
[ROW][C]Cosine[/C][C]763.933240027229[/C][C]0.0017948312434571[/C][/ROW]
[ROW][C]Optcosine[/C][C]776.949054670848[/C][C]0.00178030690124362[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206469&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular796.4727766362750.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362






Maximum Density Values
Kernelx-valuemax. density
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular799.726730297180.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 754.171379044515 & 0.0018308121967368 \tabularnewline
Epanechnikov & 776.949054670848 & 0.0017805043023184 \tabularnewline
Rectangular & 799.72673029718 & 0.00185922053832057 \tabularnewline
Triangular & 744.409518061802 & 0.00178414378749848 \tabularnewline
Biweight & 767.187193688134 & 0.00178868959247452 \tabularnewline
Cosine & 763.933240027229 & 0.0017948312434571 \tabularnewline
Optcosine & 776.949054670848 & 0.00178030690124362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=206469&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]754.171379044515[/C][C]0.0018308121967368[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]776.949054670848[/C][C]0.0017805043023184[/C][/ROW]
[ROW][C]Rectangular[/C][C]799.72673029718[/C][C]0.00185922053832057[/C][/ROW]
[ROW][C]Triangular[/C][C]744.409518061802[/C][C]0.00178414378749848[/C][/ROW]
[ROW][C]Biweight[/C][C]767.187193688134[/C][C]0.00178868959247452[/C][/ROW]
[ROW][C]Cosine[/C][C]763.933240027229[/C][C]0.0017948312434571[/C][/ROW]
[ROW][C]Optcosine[/C][C]776.949054670848[/C][C]0.00178030690124362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=206469&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=206469&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
Gaussian754.1713790445150.0018308121967368
Epanechnikov776.9490546708480.0017805043023184
Rectangular799.726730297180.00185922053832057
Triangular744.4095180618020.00178414378749848
Biweight767.1871936881340.00178868959247452
Cosine763.9332400272290.0017948312434571
Optcosine776.9490546708480.00178030690124362


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')
}