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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, 16 Feb 2014 09:27:15 -0500
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/Feb/16/t139256091917ngpk2e7m0fd3j.htm/, Retrieved Wed, 15 May 2024 16:10:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233748, Retrieved Wed, 15 May 2024 16:10:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
611.22
613.36
592.49
528.18
525.3
474
485
510
523.54
525
516.6
526.31
535
545.7
525.25
526.42
576.2
593
582.07
570.22
572.8
600.55
610
620.03
623.34
610.16
603.6
607.57
626.06
614.8
596.48
632.05
628.01
621.88
627.64
579.37
587.76
608
593.32
595.09
586.72
583.72
525.18
509.85
527.25
540.35
517.96
510.8
534.56
504
553.43
562.98
582.54
650.02
624.99
585.99
579.98
599.33
605.91
604.64
609.90
621.25
600.25
625.04
642.59
641.24
632.32
624.60
596.06
614.98
596.97
605.23
600.40
591.53
570.98
580.45
564.51
571.48
580.07
585.98
576.52
610.82
634.96
641.33
642.00
677.14
678.63
685.09
706.15
709.68
733.99
754.50
767.65
744.75
681.79
675.15
687.92
687.92
663.03
647.18
667.97
698.37
684.21
701.96
715.63
700.01
737.97
739.99
704.51
753.67
775.60
785.37
792.89
799.71
806.19
831.52
814.30
810.31
794.19
783.05
790.05
799.87
801.42
845.72
880.23
909.18
873.32
871.22
879.73
875.04
880.93
880.37
893.49
923.00
896.60
885.35
906.57
890.41
856.91
870.21
846.90
879.58
889.07
903.11
876.39
872.35
871.99
1011.41
1015.20
1027.04
1016.03
1033.56
1031.89
1059.59
1069.87
1060.79
1100.62
1118.40
1105.00

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 6 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233748&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233748&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233748&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 time6 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth50.6329088194793
#Observations159

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 50.6329088194793 \tabularnewline
#Observations & 159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233748&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]50.6329088194793[/C][/ROW]
[ROW][C]#Observations[/C][C]159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233748&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233748&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
Bandwidth50.6329088194793
#Observations159






Maximum Density Values
Kernelx-valuemax. density
Gaussian600.4371207774360.00343658350902884
Epanechnikov602.2926930923410.00327869910986784
Rectangular598.581548462530.0032379025738807
Triangular602.2926930923410.00340158054711614
Biweight600.4371207774360.00331845192349897
Cosine600.4371207774360.00333569013363812
Optcosine602.2926930923410.00329266001843572

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 600.437120777436 & 0.00343658350902884 \tabularnewline
Epanechnikov & 602.292693092341 & 0.00327869910986784 \tabularnewline
Rectangular & 598.58154846253 & 0.0032379025738807 \tabularnewline
Triangular & 602.292693092341 & 0.00340158054711614 \tabularnewline
Biweight & 600.437120777436 & 0.00331845192349897 \tabularnewline
Cosine & 600.437120777436 & 0.00333569013363812 \tabularnewline
Optcosine & 602.292693092341 & 0.00329266001843572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233748&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]600.437120777436[/C][C]0.00343658350902884[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]602.292693092341[/C][C]0.00327869910986784[/C][/ROW]
[ROW][C]Rectangular[/C][C]598.58154846253[/C][C]0.0032379025738807[/C][/ROW]
[ROW][C]Triangular[/C][C]602.292693092341[/C][C]0.00340158054711614[/C][/ROW]
[ROW][C]Biweight[/C][C]600.437120777436[/C][C]0.00331845192349897[/C][/ROW]
[ROW][C]Cosine[/C][C]600.437120777436[/C][C]0.00333569013363812[/C][/ROW]
[ROW][C]Optcosine[/C][C]602.292693092341[/C][C]0.00329266001843572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233748&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233748&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
Gaussian600.4371207774360.00343658350902884
Epanechnikov602.2926930923410.00327869910986784
Rectangular598.581548462530.0032379025738807
Triangular602.2926930923410.00340158054711614
Biweight600.4371207774360.00331845192349897
Cosine600.4371207774360.00333569013363812
Optcosine602.2926930923410.00329266001843572


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')
}