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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, 20 Aug 2013 05:09:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/20/t1376989838gd82palhia5oipq.htm/, Retrieved Sat, 27 Apr 2024 07:05:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211242, Retrieved Sat, 27 Apr 2024 07:05:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

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] [] [2013-08-20 09:09:45] [bdb7c0ed7ba273e65f9ee772c5dda4f0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1165010
1160665
1156265
1147162.5
1237238.75
1232481.25
1165010
1120157.5
1124488.75
1124488.75
1129328.75
1138005
1151507.5
1151507.5
1142831.25
1120157.5
1237238.75
1255086.25
1228136.25
1165010
1192015
1151507.5
1169781.25
1178512.5
1187615
1165010
1169781.25
1138005
1237238.75
1268588.75
1241638.75
1192015
1245983.75
1187615
1241638.75
1237238.75
1250755
1201131.25
1255086.25
1250755
1331715
1313441.25
1241638.75
1205462.5
1255086.25
1187615
1237238.75
1245983.75
1264257.5
1223805
1245983.75
1259486.25
1309110
1268588.75
1214633.75
1156265
1210288.75
1061788.75
1133660
1174112.5
1214633.75
1156265
1156265
1156265
1187615
1142831.25
1084036.25
1034838.75
1070533.75
931205
1016578.75
1066188.75
1075305
1025681.25
1030012.5
1016578.75
1061788.75
1030012.5
967381.25
922102.5
998662.5
832383.75
940362.5
989560
989560
931205
877236.25
872905
922102.5
877236.25
791931.25
733136.25
796276.25
647831.25
782760
854562.5
877236.25
827626.25
764926.25
809778.75
827626.25
814110
679126.25
616481.25
661278.75
526350
665678.75
715302.5
755755
688283.75
625157.5
661278.75
679126.25
643431.25
508502.5
449707.5
503676.25
355231.25
517178.75
616481.25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211242&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]7 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=211242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211242&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 time7 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth80070.821299504
#Observations120

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 80070.821299504 \tabularnewline
#Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211242&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]80070.821299504[/C][/ROW]
[ROW][C]#Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211242&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
Bandwidth80070.821299504
#Observations120






Maximum Density Values
Kernelx-valuemax. density
Gaussian1184178.774700092.36377290113705e-06
Epanechnikov1172774.401488372.23859152391146e-06
Rectangular1132859.095247352.24908101442255e-06
Triangular1169923.308185442.29961248770618e-06
Biweight1178476.588094232.27531853913972e-06
Cosine1181327.681397162.28864368508437e-06
Optcosine1175625.49479132.24931736466759e-06

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1184178.77470009 & 2.36377290113705e-06 \tabularnewline
Epanechnikov & 1172774.40148837 & 2.23859152391146e-06 \tabularnewline
Rectangular & 1132859.09524735 & 2.24908101442255e-06 \tabularnewline
Triangular & 1169923.30818544 & 2.29961248770618e-06 \tabularnewline
Biweight & 1178476.58809423 & 2.27531853913972e-06 \tabularnewline
Cosine & 1181327.68139716 & 2.28864368508437e-06 \tabularnewline
Optcosine & 1175625.4947913 & 2.24931736466759e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211242&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]1184178.77470009[/C][C]2.36377290113705e-06[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1172774.40148837[/C][C]2.23859152391146e-06[/C][/ROW]
[ROW][C]Rectangular[/C][C]1132859.09524735[/C][C]2.24908101442255e-06[/C][/ROW]
[ROW][C]Triangular[/C][C]1169923.30818544[/C][C]2.29961248770618e-06[/C][/ROW]
[ROW][C]Biweight[/C][C]1178476.58809423[/C][C]2.27531853913972e-06[/C][/ROW]
[ROW][C]Cosine[/C][C]1181327.68139716[/C][C]2.28864368508437e-06[/C][/ROW]
[ROW][C]Optcosine[/C][C]1175625.4947913[/C][C]2.24931736466759e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211242&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
Gaussian1184178.774700092.36377290113705e-06
Epanechnikov1172774.401488372.23859152391146e-06
Rectangular1132859.095247352.24908101442255e-06
Triangular1169923.308185442.29961248770618e-06
Biweight1178476.588094232.27531853913972e-06
Cosine1181327.681397162.28864368508437e-06
Optcosine1175625.49479132.24931736466759e-06


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')
}