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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 computationMon, 15 Dec 2014 17:42:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/15/t1418665349g8u71xf6i9wbazt.htm/, Retrieved Thu, 16 May 2024 10:10:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268801, Retrieved Thu, 16 May 2024 10:10:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Cronbach Alpha] [] [2014-12-14 22:25:21] [2b9d0c54c8c845c625e475ed5f1f3af1]
-    D  [Cronbach Alpha] [] [2014-12-14 23:28:38] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RMPD    [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 13:26:13] [2b9d0c54c8c845c625e475ed5f1f3af1]
-    D      [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 14:08:02] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM          [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 14:08:41] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM D          [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 16:14:57] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RMP             [Percentiles] [] [2014-12-15 16:22:39] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                [Tukey lambda PPCC Plot] [] [2014-12-15 16:26:30] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RMP                 [Kernel Density Estimation] [] [2014-12-15 16:30:20] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RMP                   [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 16:35:22] [2b9d0c54c8c845c625e475ed5f1f3af1]
- R  D                    [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 17:24:27] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RMP                       [Percentiles] [] [2014-12-15 17:27:50] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                          [Percentiles] [] [2014-12-15 17:28:11] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                            [Tukey lambda PPCC Plot] [] [2014-12-15 17:35:55] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                              [Kernel Density Estimation] [] [2014-12-15 17:40:21] [2b9d0c54c8c845c625e475ed5f1f3af1]
-                                     [Kernel Density Estimation] [] [2014-12-15 17:42:13] [b22ed12f8980e34362f6926e9ebd1315] [Current]
- RM D                                  [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 17:47:00] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                                      [Percentiles] [] [2014-12-15 17:50:51] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                                        [Tukey lambda PPCC Plot] [] [2014-12-15 17:56:56] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM                                        [Kernel Density Estimation] [] [2014-12-15 18:08:51] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM D                                        [Maximum-likelihood Fitting - Normal Distribution] [] [2014-12-15 18:36:43] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM D                                        [Percentiles] [] [2014-12-15 18:50:26] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM D                                        [Tukey lambda PPCC Plot] [] [2014-12-15 18:51:10] [2b9d0c54c8c845c625e475ed5f1f3af1]
- RM D                                          [Notched Boxplots] [] [2014-12-15 19:44:02] [2b9d0c54c8c845c625e475ed5f1f3af1]
-    D                                        [Kernel Density Estimation] [] [2014-12-15 18:53:06] [2b9d0c54c8c845c625e475ed5f1f3af1]
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Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12
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15
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15
28
11
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28
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15
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17
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23
16
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25
18
14
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18
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21
14
5
25
21
11
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9
15
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21
9
24
16
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15
18
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21
21
21
20
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15
24
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24
15
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20
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26
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13
16
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21
11
23
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15
8
15
21
25
14
21
18
18
12
24
17
20
24
22
15
22
26
17
23
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21
23
19
18
16
23
13
18
23
21
23
16
17
20
18
20
19
26
9
23
9
13
27
22
12
18
6
17
22
22
23
19
20
17
24
20
18
23
27
25
24
12
16
24
23
24
24
26
19
28
23
21
19
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23
20
18
20
28
21
25
18
24
28
9
22
26
28
18
23
15
24
12
12
20
25
24
23
18
20
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20
25
28
25
14
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13
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8
27
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20
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15
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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 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=268801&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=268801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268801&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
Bandwidth1.089679438726
#Observations278

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.089679438726 \tabularnewline
#Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268801&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.089679438726[/C][/ROW]
[ROW][C]#Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268801&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268801&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
Bandwidth1.089679438726
#Observations278






Maximum Density Values
Kernelx-valuemax. density
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.32667201331060.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 20.8642363713168 & 0.0966834434318602 \tabularnewline
Epanechnikov & 21.9047165658029 & 0.0975674331816756 \tabularnewline
Rectangular & 21.3266720133106 & 0.103870524057838 \tabularnewline
Triangular & 21.0376497370645 & 0.0983366739350194 \tabularnewline
Biweight & 21.1532586475629 & 0.095880651994725 \tabularnewline
Cosine & 21.3266720133106 & 0.0959488411382193 \tabularnewline
Optcosine & 21.9047165658029 & 0.0970783809792169 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268801&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]20.8642363713168[/C][C]0.0966834434318602[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.9047165658029[/C][C]0.0975674331816756[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.3266720133106[/C][C]0.103870524057838[/C][/ROW]
[ROW][C]Triangular[/C][C]21.0376497370645[/C][C]0.0983366739350194[/C][/ROW]
[ROW][C]Biweight[/C][C]21.1532586475629[/C][C]0.095880651994725[/C][/ROW]
[ROW][C]Cosine[/C][C]21.3266720133106[/C][C]0.0959488411382193[/C][/ROW]
[ROW][C]Optcosine[/C][C]21.9047165658029[/C][C]0.0970783809792169[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268801&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268801&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
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.32667201331060.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169






Maximum Density Values
Kernelx-valuemax. density
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.38447646855980.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 20.8642363713168 & 0.0966834434318602 \tabularnewline
Epanechnikov & 21.9047165658029 & 0.0975674331816756 \tabularnewline
Rectangular & 21.3844764685598 & 0.103870524057838 \tabularnewline
Triangular & 21.0376497370645 & 0.0983366739350194 \tabularnewline
Biweight & 21.1532586475629 & 0.095880651994725 \tabularnewline
Cosine & 21.3266720133106 & 0.0959488411382193 \tabularnewline
Optcosine & 21.9047165658029 & 0.0970783809792169 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268801&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]20.8642363713168[/C][C]0.0966834434318602[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.9047165658029[/C][C]0.0975674331816756[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.3844764685598[/C][C]0.103870524057838[/C][/ROW]
[ROW][C]Triangular[/C][C]21.0376497370645[/C][C]0.0983366739350194[/C][/ROW]
[ROW][C]Biweight[/C][C]21.1532586475629[/C][C]0.095880651994725[/C][/ROW]
[ROW][C]Cosine[/C][C]21.3266720133106[/C][C]0.0959488411382193[/C][/ROW]
[ROW][C]Optcosine[/C][C]21.9047165658029[/C][C]0.0970783809792169[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268801&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268801&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
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.38447646855980.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169






Maximum Density Values
Kernelx-valuemax. density
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.61569428955680.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 20.8642363713168 & 0.0966834434318602 \tabularnewline
Epanechnikov & 21.9047165658029 & 0.0975674331816756 \tabularnewline
Rectangular & 21.6156942895568 & 0.103870524057838 \tabularnewline
Triangular & 21.0376497370645 & 0.0983366739350194 \tabularnewline
Biweight & 21.1532586475629 & 0.095880651994725 \tabularnewline
Cosine & 21.3266720133106 & 0.0959488411382193 \tabularnewline
Optcosine & 21.9047165658029 & 0.0970783809792169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268801&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]20.8642363713168[/C][C]0.0966834434318602[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]21.9047165658029[/C][C]0.0975674331816756[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.6156942895568[/C][C]0.103870524057838[/C][/ROW]
[ROW][C]Triangular[/C][C]21.0376497370645[/C][C]0.0983366739350194[/C][/ROW]
[ROW][C]Biweight[/C][C]21.1532586475629[/C][C]0.095880651994725[/C][/ROW]
[ROW][C]Cosine[/C][C]21.3266720133106[/C][C]0.0959488411382193[/C][/ROW]
[ROW][C]Optcosine[/C][C]21.9047165658029[/C][C]0.0970783809792169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268801&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268801&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
Gaussian20.86423637131680.0966834434318602
Epanechnikov21.90471656580290.0975674331816756
Rectangular21.61569428955680.103870524057838
Triangular21.03764973706450.0983366739350194
Biweight21.15325864756290.095880651994725
Cosine21.32667201331060.0959488411382193
Optcosine21.90471656580290.0970783809792169


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
}