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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 Aug 2014 16:01:25 +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/2014/Aug/12/t1407855720h51eyb2d323odyd.htm/, Retrieved Thu, 16 May 2024 06:25:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235487, Retrieved Thu, 16 May 2024 06:25:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2014-08-12 14:49:48] [ba0170e6f15797e8c541ec0953bc1848]
- RMP     [Kernel Density Estimation] [] [2014-08-12 15:01:25] [b3e3d38149b35cb70244b37a39776b3a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106
105
104
102
122
121
106
96
97
97
98
100
106
104
107
112
140
140
134
128
133
139
140
143
152
146
146
155
180
182
177
165
174
174
175
180
184
186
186
192
215
221
222
207
215
212
206
219
222
217
218
225
251
264
264
258
267
258
253
272
275
268
286
293
314
328
326
325
333
332
320
338
344
338
363
375
403
414
411
405
410
416
396
412
422
418
444
453
491
498
489
494
497
500
481
499
509
499
528
537
576
582
584
594
594
598
580
589
595
584
616
622
662
669
679
688
689
690
672
690

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235487&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235487&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'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth63.1436566889191
#Observations120

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 63.1436566889191 \tabularnewline
#Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235487&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]63.1436566889191[/C][/ROW]
[ROW][C]#Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235487&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
Bandwidth63.1436566889191
#Observations120






Maximum Density Values
Kernelx-valuemax. density
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular194.048781322990.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 173.106547778041 & 0.0023883760936709 \tabularnewline
Epanechnikov & 180.72190543075 & 0.00235182340978442 \tabularnewline
Rectangular & 194.04878132299 & 0.00243825080549886 \tabularnewline
Triangular & 182.625744843927 & 0.0023532438044296 \tabularnewline
Biweight & 182.625744843927 & 0.00236267789973393 \tabularnewline
Cosine & 180.72190543075 & 0.00236541454478612 \tabularnewline
Optcosine & 186.433423670281 & 0.00235183228452234 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235487&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]173.106547778041[/C][C]0.0023883760936709[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]180.72190543075[/C][C]0.00235182340978442[/C][/ROW]
[ROW][C]Rectangular[/C][C]194.04878132299[/C][C]0.00243825080549886[/C][/ROW]
[ROW][C]Triangular[/C][C]182.625744843927[/C][C]0.0023532438044296[/C][/ROW]
[ROW][C]Biweight[/C][C]182.625744843927[/C][C]0.00236267789973393[/C][/ROW]
[ROW][C]Cosine[/C][C]180.72190543075[/C][C]0.00236541454478612[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.433423670281[/C][C]0.00235183228452234[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235487&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235487&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
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular194.048781322990.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234






Maximum Density Values
Kernelx-valuemax. density
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular195.9526207361670.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 173.106547778041 & 0.0023883760936709 \tabularnewline
Epanechnikov & 180.72190543075 & 0.00235182340978442 \tabularnewline
Rectangular & 195.952620736167 & 0.00243825080549886 \tabularnewline
Triangular & 182.625744843927 & 0.0023532438044296 \tabularnewline
Biweight & 182.625744843927 & 0.00236267789973393 \tabularnewline
Cosine & 180.72190543075 & 0.00236541454478612 \tabularnewline
Optcosine & 186.433423670281 & 0.00235183228452234 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235487&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]173.106547778041[/C][C]0.0023883760936709[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]180.72190543075[/C][C]0.00235182340978442[/C][/ROW]
[ROW][C]Rectangular[/C][C]195.952620736167[/C][C]0.00243825080549886[/C][/ROW]
[ROW][C]Triangular[/C][C]182.625744843927[/C][C]0.0023532438044296[/C][/ROW]
[ROW][C]Biweight[/C][C]182.625744843927[/C][C]0.00236267789973393[/C][/ROW]
[ROW][C]Cosine[/C][C]180.72190543075[/C][C]0.00236541454478612[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.433423670281[/C][C]0.00235183228452234[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235487&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235487&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
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular195.9526207361670.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234






Maximum Density Values
Kernelx-valuemax. density
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular197.8564601493440.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 173.106547778041 & 0.0023883760936709 \tabularnewline
Epanechnikov & 180.72190543075 & 0.00235182340978442 \tabularnewline
Rectangular & 197.856460149344 & 0.00243825080549886 \tabularnewline
Triangular & 182.625744843927 & 0.0023532438044296 \tabularnewline
Biweight & 182.625744843927 & 0.00236267789973393 \tabularnewline
Cosine & 180.72190543075 & 0.00236541454478612 \tabularnewline
Optcosine & 186.433423670281 & 0.00235183228452234 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235487&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]173.106547778041[/C][C]0.0023883760936709[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]180.72190543075[/C][C]0.00235182340978442[/C][/ROW]
[ROW][C]Rectangular[/C][C]197.856460149344[/C][C]0.00243825080549886[/C][/ROW]
[ROW][C]Triangular[/C][C]182.625744843927[/C][C]0.0023532438044296[/C][/ROW]
[ROW][C]Biweight[/C][C]182.625744843927[/C][C]0.00236267789973393[/C][/ROW]
[ROW][C]Cosine[/C][C]180.72190543075[/C][C]0.00236541454478612[/C][/ROW]
[ROW][C]Optcosine[/C][C]186.433423670281[/C][C]0.00235183228452234[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235487&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235487&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
Gaussian173.1065477780410.0023883760936709
Epanechnikov180.721905430750.00235182340978442
Rectangular197.8564601493440.00243825080549886
Triangular182.6257448439270.0023532438044296
Biweight182.6257448439270.00236267789973393
Cosine180.721905430750.00236541454478612
Optcosine186.4334236702810.00235183228452234


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')
}