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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 computationSun, 28 Dec 2014 22:22:58 +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/28/t1419805436ds1ivhc996b7k6h.htm/, Retrieved Sun, 19 May 2024 15:52:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271616, Retrieved Sun, 19 May 2024 15:52:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124

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] [] [2014-12-28 22:22:58] [6bc6bd52ef4ec9e5c067ef01cf67dcff] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3004
3080
3017
3114
3057
3032
3127
3050
2910
2671
2638
2672
2654
2568
2467
2419
2363
2291
2560
2527
2370
2310
2231
2367
2346
2286
2249
2226
2108
2131
2387
2358
2284
2312
2293
2576
2665
2749
2926
2886
2893
2944
3060
3045
2894
2955
2954
3243
3120
3074
3034
2981
2876
2835
2978
2881
2768
2722
2630
2753
2771
2652
2584
2501
2449
2445
2620
2579
2460
2434
2392
1037
1212
1232
1174
1158
1140
1118
1212
1207
1186
608
627
626
649
619
612
643
623
649
699
693
659
669
668
693

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271616&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271616&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271616&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth307.725067663141
#Observations96

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 307.725067663141 \tabularnewline
#Observations & 96 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271616&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]307.725067663141[/C][/ROW]
[ROW][C]#Observations[/C][C]96[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271616&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271616&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
Bandwidth307.725067663141
#Observations96






Maximum Density Values
Kernelx-valuemax. density
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2605.156861963520.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2666.54522368926 & 0.000648325621392938 \tabularnewline
Epanechnikov & 2675.31498965008 & 0.000656365503929406 \tabularnewline
Rectangular & 2605.15686196352 & 0.000684027100036166 \tabularnewline
Triangular & 2657.77545772844 & 0.000645368245876859 \tabularnewline
Biweight & 2675.31498965008 & 0.000652219925160194 \tabularnewline
Cosine & 2675.31498965008 & 0.000650783037587406 \tabularnewline
Optcosine & 2675.31498965008 & 0.000654301378806325 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271616&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]2666.54522368926[/C][C]0.000648325621392938[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2675.31498965008[/C][C]0.000656365503929406[/C][/ROW]
[ROW][C]Rectangular[/C][C]2605.15686196352[/C][C]0.000684027100036166[/C][/ROW]
[ROW][C]Triangular[/C][C]2657.77545772844[/C][C]0.000645368245876859[/C][/ROW]
[ROW][C]Biweight[/C][C]2675.31498965008[/C][C]0.000652219925160194[/C][/ROW]
[ROW][C]Cosine[/C][C]2675.31498965008[/C][C]0.000650783037587406[/C][/ROW]
[ROW][C]Optcosine[/C][C]2675.31498965008[/C][C]0.000654301378806325[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271616&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271616&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
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2605.156861963520.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325






Maximum Density Values
Kernelx-valuemax. density
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2613.926627924340.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2666.54522368926 & 0.000648325621392938 \tabularnewline
Epanechnikov & 2675.31498965008 & 0.000656365503929406 \tabularnewline
Rectangular & 2613.92662792434 & 0.000684027100036166 \tabularnewline
Triangular & 2657.77545772844 & 0.000645368245876859 \tabularnewline
Biweight & 2675.31498965008 & 0.000652219925160194 \tabularnewline
Cosine & 2675.31498965008 & 0.000650783037587406 \tabularnewline
Optcosine & 2675.31498965008 & 0.000654301378806325 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271616&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]2666.54522368926[/C][C]0.000648325621392938[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2675.31498965008[/C][C]0.000656365503929406[/C][/ROW]
[ROW][C]Rectangular[/C][C]2613.92662792434[/C][C]0.000684027100036166[/C][/ROW]
[ROW][C]Triangular[/C][C]2657.77545772844[/C][C]0.000645368245876859[/C][/ROW]
[ROW][C]Biweight[/C][C]2675.31498965008[/C][C]0.000652219925160194[/C][/ROW]
[ROW][C]Cosine[/C][C]2675.31498965008[/C][C]0.000650783037587406[/C][/ROW]
[ROW][C]Optcosine[/C][C]2675.31498965008[/C][C]0.000654301378806325[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271616&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271616&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
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2613.926627924340.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325






Maximum Density Values
Kernelx-valuemax. density
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2622.696393885160.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2666.54522368926 & 0.000648325621392938 \tabularnewline
Epanechnikov & 2675.31498965008 & 0.000656365503929406 \tabularnewline
Rectangular & 2622.69639388516 & 0.000684027100036166 \tabularnewline
Triangular & 2657.77545772844 & 0.000645368245876859 \tabularnewline
Biweight & 2675.31498965008 & 0.000652219925160194 \tabularnewline
Cosine & 2675.31498965008 & 0.000650783037587406 \tabularnewline
Optcosine & 2675.31498965008 & 0.000654301378806325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271616&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]2666.54522368926[/C][C]0.000648325621392938[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2675.31498965008[/C][C]0.000656365503929406[/C][/ROW]
[ROW][C]Rectangular[/C][C]2622.69639388516[/C][C]0.000684027100036166[/C][/ROW]
[ROW][C]Triangular[/C][C]2657.77545772844[/C][C]0.000645368245876859[/C][/ROW]
[ROW][C]Biweight[/C][C]2675.31498965008[/C][C]0.000652219925160194[/C][/ROW]
[ROW][C]Cosine[/C][C]2675.31498965008[/C][C]0.000650783037587406[/C][/ROW]
[ROW][C]Optcosine[/C][C]2675.31498965008[/C][C]0.000654301378806325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271616&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271616&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
Gaussian2666.545223689260.000648325621392938
Epanechnikov2675.314989650080.000656365503929406
Rectangular2622.696393885160.000684027100036166
Triangular2657.775457728440.000645368245876859
Biweight2675.314989650080.000652219925160194
Cosine2675.314989650080.000650783037587406
Optcosine2675.314989650080.000654301378806325


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')
}