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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationTue, 16 Oct 2012 14:46:45 -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/2012/Oct/16/t1350413269u6wsdqgjazbv2wc.htm/, Retrieved Tue, 30 Apr 2024 17:08:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179146, Retrieved Tue, 30 Apr 2024 17:08:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact52

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] [WS3 T3] [2012-10-16 18:46:45] [6b9eda33bf4cae06c9f9f024b199ddfb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4
4
6
8
8
4
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8
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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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth0.728376562744723
#Observations162

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.728376562744723 \tabularnewline
#Observations & 162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.728376562744723[/C][/ROW]
[ROW][C]#Observations[/C][C]162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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
Bandwidth0.728376562744723
#Observations162






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular4.942487857270230.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.15159606415417 & 0.297901896675347 \tabularnewline
Epanechnikov & 4.22349531807381 & 0.265792452672358 \tabularnewline
Rectangular & 4.94248785727023 & 0.2837895430808 \tabularnewline
Triangular & 4.00779755631489 & 0.300954958819258 \tabularnewline
Biweight & 4.25944494503363 & 0.275430652402884 \tabularnewline
Cosine & 4.22349531807381 & 0.278978312894587 \tabularnewline
Optcosine & 4.18754569111399 & 0.268476597426866 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&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]4.15159606415417[/C][C]0.297901896675347[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.22349531807381[/C][C]0.265792452672358[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.94248785727023[/C][C]0.2837895430808[/C][/ROW]
[ROW][C]Triangular[/C][C]4.00779755631489[/C][C]0.300954958819258[/C][/ROW]
[ROW][C]Biweight[/C][C]4.25944494503363[/C][C]0.275430652402884[/C][/ROW]
[ROW][C]Cosine[/C][C]4.22349531807381[/C][C]0.278978312894587[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.18754569111399[/C][C]0.268476597426866[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular4.942487857270230.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular4.978437484230050.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.15159606415417 & 0.297901896675347 \tabularnewline
Epanechnikov & 4.22349531807381 & 0.265792452672358 \tabularnewline
Rectangular & 4.97843748423005 & 0.2837895430808 \tabularnewline
Triangular & 4.00779755631489 & 0.300954958819258 \tabularnewline
Biweight & 4.25944494503363 & 0.275430652402884 \tabularnewline
Cosine & 4.22349531807381 & 0.278978312894587 \tabularnewline
Optcosine & 4.18754569111399 & 0.268476597426866 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&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]4.15159606415417[/C][C]0.297901896675347[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.22349531807381[/C][C]0.265792452672358[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.97843748423005[/C][C]0.2837895430808[/C][/ROW]
[ROW][C]Triangular[/C][C]4.00779755631489[/C][C]0.300954958819258[/C][/ROW]
[ROW][C]Biweight[/C][C]4.25944494503363[/C][C]0.275430652402884[/C][/ROW]
[ROW][C]Cosine[/C][C]4.22349531807381[/C][C]0.278978312894587[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.18754569111399[/C][C]0.268476597426866[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular4.978437484230050.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.014387111189870.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.15159606415417 & 0.297901896675347 \tabularnewline
Epanechnikov & 4.22349531807381 & 0.265792452672358 \tabularnewline
Rectangular & 5.01438711118987 & 0.2837895430808 \tabularnewline
Triangular & 4.00779755631489 & 0.300954958819258 \tabularnewline
Biweight & 4.25944494503363 & 0.275430652402884 \tabularnewline
Cosine & 4.22349531807381 & 0.278978312894587 \tabularnewline
Optcosine & 4.18754569111399 & 0.268476597426866 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&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]4.15159606415417[/C][C]0.297901896675347[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.22349531807381[/C][C]0.265792452672358[/C][/ROW]
[ROW][C]Rectangular[/C][C]5.01438711118987[/C][C]0.2837895430808[/C][/ROW]
[ROW][C]Triangular[/C][C]4.00779755631489[/C][C]0.300954958819258[/C][/ROW]
[ROW][C]Biweight[/C][C]4.25944494503363[/C][C]0.275430652402884[/C][/ROW]
[ROW][C]Cosine[/C][C]4.22349531807381[/C][C]0.278978312894587[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.18754569111399[/C][C]0.268476597426866[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.014387111189870.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.050336738149690.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.15159606415417 & 0.297901896675347 \tabularnewline
Epanechnikov & 4.22349531807381 & 0.265792452672358 \tabularnewline
Rectangular & 5.05033673814969 & 0.2837895430808 \tabularnewline
Triangular & 4.00779755631489 & 0.300954958819258 \tabularnewline
Biweight & 4.25944494503363 & 0.275430652402884 \tabularnewline
Cosine & 4.22349531807381 & 0.278978312894587 \tabularnewline
Optcosine & 4.18754569111399 & 0.268476597426866 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&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]4.15159606415417[/C][C]0.297901896675347[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.22349531807381[/C][C]0.265792452672358[/C][/ROW]
[ROW][C]Rectangular[/C][C]5.05033673814969[/C][C]0.2837895430808[/C][/ROW]
[ROW][C]Triangular[/C][C]4.00779755631489[/C][C]0.300954958819258[/C][/ROW]
[ROW][C]Biweight[/C][C]4.25944494503363[/C][C]0.275430652402884[/C][/ROW]
[ROW][C]Cosine[/C][C]4.22349531807381[/C][C]0.278978312894587[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.18754569111399[/C][C]0.268476597426866[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&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
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.050336738149690.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.194135245988970.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.15159606415417 & 0.297901896675347 \tabularnewline
Epanechnikov & 4.22349531807381 & 0.265792452672358 \tabularnewline
Rectangular & 5.19413524598897 & 0.2837895430808 \tabularnewline
Triangular & 4.00779755631489 & 0.300954958819258 \tabularnewline
Biweight & 4.25944494503363 & 0.275430652402884 \tabularnewline
Cosine & 4.22349531807381 & 0.278978312894587 \tabularnewline
Optcosine & 4.18754569111399 & 0.268476597426866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179146&T=6

[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]4.15159606415417[/C][C]0.297901896675347[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.22349531807381[/C][C]0.265792452672358[/C][/ROW]
[ROW][C]Rectangular[/C][C]5.19413524598897[/C][C]0.2837895430808[/C][/ROW]
[ROW][C]Triangular[/C][C]4.00779755631489[/C][C]0.300954958819258[/C][/ROW]
[ROW][C]Biweight[/C][C]4.25944494503363[/C][C]0.275430652402884[/C][/ROW]
[ROW][C]Cosine[/C][C]4.22349531807381[/C][C]0.278978312894587[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.18754569111399[/C][C]0.268476597426866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179146&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179146&T=6

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
Gaussian4.151596064154170.297901896675347
Epanechnikov4.223495318073810.265792452672358
Rectangular5.194135245988970.2837895430808
Triangular4.007797556314890.300954958819258
Biweight4.259444945033630.275430652402884
Cosine4.223495318073810.278978312894587
Optcosine4.187545691113990.268476597426866


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 200 ; par2 = 5 ; par3 = 0 ;
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')
}