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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 computationSat, 09 Aug 2014 17:26:48 +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/09/t1407601682j335tyfdl5a0x8i.htm/, Retrieved Fri, 17 May 2024 05:21:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235431, Retrieved Fri, 17 May 2024 05:21:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBoeykens Brice
Estimated Impact160

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [Tijdreeks A Stap 3] [2014-08-09 15:40:12] [2064a7ed2562130dd70fccaf2dd61d5a]
- RM      [Kernel Density Estimation] [Tijdreeks A Stap 6] [2014-08-09 16:26:48] [7314f5de623f4497f735e8af2050bf2f] [Current]
- RMP       [Univariate Data Series] [] [2016-09-10 18:50:39] [597f04887712160a284bcf6998091a8a]
- RMP       [Moments] [] [2016-09-10 18:52:52] [597f04887712160a284bcf6998091a8a]
- RMPD        [Histogram] [] [2016-09-10 19:02:38] [597f04887712160a284bcf6998091a8a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5115
5105
5094
5074
5280
5270
5115
5012
5022
5022
5032
5053
5053
4960
4919
4960
5105
5084
4888
4722
4691
4629
4671
4722
4702
4660
4578
4660
4733
4712
4474
4371
4268
4185
4175
4237
4154
4123
4092
4268
4288
4185
3906
3782
3586
3503
3544
3606
3606
3555
3544
3710
3844
3782
3575
3472
3255
3121
3224
3327
3327
3193
3183
3358
3472
3431
3224
3090
2800
2687
2728
2904
2914
2656
2749
2976
3079
3017
2738
2542
2315
2139
2211
2366
2325
2098
2170
2397
2521
2449
2170
2046
1860
1664
1695
1850
1870
1684
1715
1974
2036
1932
1550
1354
1095
837
920
1033
1013
816
930
1209
1333
1271
1023
827
620
382
424
496

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=235431&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=235431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235431&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
Bandwidth481.153406880733
#Observations120

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 481.153406880733 \tabularnewline
#Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235431&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]481.153406880733[/C][/ROW]
[ROW][C]#Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235431&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
Bandwidth481.153406880733
#Observations120






Maximum Density Values
Kernelx-valuemax. density
Gaussian4666.778695058260.000237135136170521
Epanechnikov4362.085135712490.000238136536543986
Rectangular4301.146423843340.000271053191738653
Triangular4270.677067908760.000232568050664902
Biweight4483.96255945080.000234676472581422
Cosine4529.666593352660.000234369830125535
Optcosine4392.554491647070.000236694754896701

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4666.77869505826 & 0.000237135136170521 \tabularnewline
Epanechnikov & 4362.08513571249 & 0.000238136536543986 \tabularnewline
Rectangular & 4301.14642384334 & 0.000271053191738653 \tabularnewline
Triangular & 4270.67706790876 & 0.000232568050664902 \tabularnewline
Biweight & 4483.9625594508 & 0.000234676472581422 \tabularnewline
Cosine & 4529.66659335266 & 0.000234369830125535 \tabularnewline
Optcosine & 4392.55449164707 & 0.000236694754896701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235431&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]4666.77869505826[/C][C]0.000237135136170521[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4362.08513571249[/C][C]0.000238136536543986[/C][/ROW]
[ROW][C]Rectangular[/C][C]4301.14642384334[/C][C]0.000271053191738653[/C][/ROW]
[ROW][C]Triangular[/C][C]4270.67706790876[/C][C]0.000232568050664902[/C][/ROW]
[ROW][C]Biweight[/C][C]4483.9625594508[/C][C]0.000234676472581422[/C][/ROW]
[ROW][C]Cosine[/C][C]4529.66659335266[/C][C]0.000234369830125535[/C][/ROW]
[ROW][C]Optcosine[/C][C]4392.55449164707[/C][C]0.000236694754896701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235431&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
Gaussian4666.778695058260.000237135136170521
Epanechnikov4362.085135712490.000238136536543986
Rectangular4301.146423843340.000271053191738653
Triangular4270.677067908760.000232568050664902
Biweight4483.96255945080.000234676472581422
Cosine4529.666593352660.000234369830125535
Optcosine4392.554491647070.000236694754896701


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')
}