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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, 30 Sep 2014 16:52:58 +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/Sep/30/t1412092464z0arcshzk1nj8kh.htm/, Retrieved Fri, 10 May 2024 07:34:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=237070, Retrieved Fri, 10 May 2024 07:34:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid België] [2014-09-24 13:54:39] [74be16979710d4c4e7c6647856088456]
- R PD  [Univariate Data Series] [Werkloosheid België] [2014-09-30 14:57:47] [b1f04123d82573d686ac8c7adc52feaa]
- RMP     [Histogram] [Werkloosheid Belg...] [2014-09-30 15:37:12] [b1f04123d82573d686ac8c7adc52feaa]
- RMP         [Kernel Density Estimation] [Dichtheidsgrafiek...] [2014-09-30 15:52:58] [c260288012d574817ee98c3ddd4d9474] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
541
562
559
546
536
528
530
582
599
584
571
563
565
578
572
565
561
551
553
611
622
613
599
591
596

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'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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=237070&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=237070&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=237070&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth11.8995587807582
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 11.8995587807582 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=237070&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]11.8995587807582[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=237070&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=237070&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
Bandwidth11.8995587807582
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian550.1109045072170.0112929674352778
Epanechnikov547.4761019316640.0115798982338804
Rectangular545.2804331187040.0127072597878393
Triangular548.793503219440.0114223588985819
Biweight547.9152356942560.0114557252301219
Cosine547.9152356942560.0114174791454331
Optcosine548.793503219440.0115365852555271

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 550.110904507217 & 0.0112929674352778 \tabularnewline
Epanechnikov & 547.476101931664 & 0.0115798982338804 \tabularnewline
Rectangular & 545.280433118704 & 0.0127072597878393 \tabularnewline
Triangular & 548.79350321944 & 0.0114223588985819 \tabularnewline
Biweight & 547.915235694256 & 0.0114557252301219 \tabularnewline
Cosine & 547.915235694256 & 0.0114174791454331 \tabularnewline
Optcosine & 548.79350321944 & 0.0115365852555271 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=237070&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]550.110904507217[/C][C]0.0112929674352778[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]547.476101931664[/C][C]0.0115798982338804[/C][/ROW]
[ROW][C]Rectangular[/C][C]545.280433118704[/C][C]0.0127072597878393[/C][/ROW]
[ROW][C]Triangular[/C][C]548.79350321944[/C][C]0.0114223588985819[/C][/ROW]
[ROW][C]Biweight[/C][C]547.915235694256[/C][C]0.0114557252301219[/C][/ROW]
[ROW][C]Cosine[/C][C]547.915235694256[/C][C]0.0114174791454331[/C][/ROW]
[ROW][C]Optcosine[/C][C]548.79350321944[/C][C]0.0115365852555271[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=237070&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=237070&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
Gaussian550.1109045072170.0112929674352778
Epanechnikov547.4761019316640.0115798982338804
Rectangular545.2804331187040.0127072597878393
Triangular548.793503219440.0114223588985819
Biweight547.9152356942560.0114557252301219
Cosine547.9152356942560.0114174791454331
Optcosine548.793503219440.0115365852555271






Maximum Density Values
Kernelx-valuemax. density
Gaussian550.1109045072170.0112929674352778
Epanechnikov547.4761019316640.0115798982338804
Rectangular545.7195668812960.0127072597878393
Triangular548.793503219440.0114223588985819
Biweight547.9152356942560.0114557252301219
Cosine547.9152356942560.0114174791454331
Optcosine548.793503219440.0115365852555271

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 550.110904507217 & 0.0112929674352778 \tabularnewline
Epanechnikov & 547.476101931664 & 0.0115798982338804 \tabularnewline
Rectangular & 545.719566881296 & 0.0127072597878393 \tabularnewline
Triangular & 548.79350321944 & 0.0114223588985819 \tabularnewline
Biweight & 547.915235694256 & 0.0114557252301219 \tabularnewline
Cosine & 547.915235694256 & 0.0114174791454331 \tabularnewline
Optcosine & 548.79350321944 & 0.0115365852555271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=237070&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]550.110904507217[/C][C]0.0112929674352778[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]547.476101931664[/C][C]0.0115798982338804[/C][/ROW]
[ROW][C]Rectangular[/C][C]545.719566881296[/C][C]0.0127072597878393[/C][/ROW]
[ROW][C]Triangular[/C][C]548.79350321944[/C][C]0.0114223588985819[/C][/ROW]
[ROW][C]Biweight[/C][C]547.915235694256[/C][C]0.0114557252301219[/C][/ROW]
[ROW][C]Cosine[/C][C]547.915235694256[/C][C]0.0114174791454331[/C][/ROW]
[ROW][C]Optcosine[/C][C]548.79350321944[/C][C]0.0115365852555271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=237070&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=237070&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
Gaussian550.1109045072170.0112929674352778
Epanechnikov547.4761019316640.0115798982338804
Rectangular545.7195668812960.0127072597878393
Triangular548.793503219440.0114223588985819
Biweight547.9152356942560.0114557252301219
Cosine547.9152356942560.0114174791454331
Optcosine548.793503219440.0115365852555271


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):
par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}