FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 17 Jul 2014 12:54:43 +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/Jul/17/t14055982178vd6540ndic20dp.htm/, Retrieved Tue, 14 May 2024 02:28:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235335, Retrieved Tue, 14 May 2024 02:28:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

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] [] [2014-07-17 11:54:43] [0b4002381e6bc6fac3755b1107da82aa] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
192528
190773
188996
185320
221698
219771
192528
174414
176163
176163
178112
181616
192528
188996
194449
203412
254400
254400
243516
232604
241567
252473
254400
259853
276217
265306
265306
281670
327033
330709
321580
299762
316121
316121
317876
327033
334241
337917
337917
348823
390681
401565
403314
376071
390681
385228
374317
397889
403314
394185
396112
408773
456085
479624
479624
468740
485082
468740
459588
494239
499664
486832
519533
532366
570521
595842
592339
590389
604999
603222
581432
614128
625040
614128
659491
681309
732102
752143
746712
735800
744935
755841
719441
748461
766753
759373
806657
822993
892101
904761
888424
897554
903007
908460
873809
906511
924624
906511
959275
975618
1046468
1057380
1060884
1079170
1079170
1086378
1053676
1070041
1080925
1060884
1119079
1129986
1202597
1215430
1233543
1249908
1251657
1253584
1220883
1253584

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'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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235335&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235335&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth114713.184179443
#Observations120

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 114713.184179443 \tabularnewline
#Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235335&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]114713.184179443[/C][/ROW]
[ROW][C]#Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235335&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
Bandwidth114713.184179443
#Observations120






Maximum Density Values
Kernelx-valuemax. density
Gaussian314507.0789895221.31460082201494e-06
Epanechnikov328342.2970331751.29449452062447e-06
Rectangular338718.7105659141.34213057448622e-06
Triangular331801.1015440881.29527952960527e-06
Biweight331801.1015440881.30046322167624e-06
Cosine328342.2970331751.3019691860606e-06
Optcosine338718.7105659141.29450426197957e-06

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 314507.078989522 & 1.31460082201494e-06 \tabularnewline
Epanechnikov & 328342.297033175 & 1.29449452062447e-06 \tabularnewline
Rectangular & 338718.710565914 & 1.34213057448622e-06 \tabularnewline
Triangular & 331801.101544088 & 1.29527952960527e-06 \tabularnewline
Biweight & 331801.101544088 & 1.30046322167624e-06 \tabularnewline
Cosine & 328342.297033175 & 1.3019691860606e-06 \tabularnewline
Optcosine & 338718.710565914 & 1.29450426197957e-06 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235335&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]314507.078989522[/C][C]1.31460082201494e-06[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]328342.297033175[/C][C]1.29449452062447e-06[/C][/ROW]
[ROW][C]Rectangular[/C][C]338718.710565914[/C][C]1.34213057448622e-06[/C][/ROW]
[ROW][C]Triangular[/C][C]331801.101544088[/C][C]1.29527952960527e-06[/C][/ROW]
[ROW][C]Biweight[/C][C]331801.101544088[/C][C]1.30046322167624e-06[/C][/ROW]
[ROW][C]Cosine[/C][C]328342.297033175[/C][C]1.3019691860606e-06[/C][/ROW]
[ROW][C]Optcosine[/C][C]338718.710565914[/C][C]1.29450426197957e-06[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235335&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
Gaussian314507.0789895221.31460082201494e-06
Epanechnikov328342.2970331751.29449452062447e-06
Rectangular338718.7105659141.34213057448622e-06
Triangular331801.1015440881.29527952960527e-06
Biweight331801.1015440881.30046322167624e-06
Cosine328342.2970331751.3019691860606e-06
Optcosine338718.7105659141.29450426197957e-06






Maximum Density Values
Kernelx-valuemax. density
Gaussian314507.0789895221.31460082201494e-06
Epanechnikov328342.2970331751.29449452062447e-06
Rectangular359471.5376313941.34213057448622e-06
Triangular331801.1015440881.29527952960527e-06
Biweight331801.1015440881.30046322167624e-06
Cosine328342.2970331751.3019691860606e-06
Optcosine338718.7105659141.29450426197957e-06

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 314507.078989522 & 1.31460082201494e-06 \tabularnewline
Epanechnikov & 328342.297033175 & 1.29449452062447e-06 \tabularnewline
Rectangular & 359471.537631394 & 1.34213057448622e-06 \tabularnewline
Triangular & 331801.101544088 & 1.29527952960527e-06 \tabularnewline
Biweight & 331801.101544088 & 1.30046322167624e-06 \tabularnewline
Cosine & 328342.297033175 & 1.3019691860606e-06 \tabularnewline
Optcosine & 338718.710565914 & 1.29450426197957e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235335&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]314507.078989522[/C][C]1.31460082201494e-06[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]328342.297033175[/C][C]1.29449452062447e-06[/C][/ROW]
[ROW][C]Rectangular[/C][C]359471.537631394[/C][C]1.34213057448622e-06[/C][/ROW]
[ROW][C]Triangular[/C][C]331801.101544088[/C][C]1.29527952960527e-06[/C][/ROW]
[ROW][C]Biweight[/C][C]331801.101544088[/C][C]1.30046322167624e-06[/C][/ROW]
[ROW][C]Cosine[/C][C]328342.297033175[/C][C]1.3019691860606e-06[/C][/ROW]
[ROW][C]Optcosine[/C][C]338718.710565914[/C][C]1.29450426197957e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235335&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235335&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
Gaussian314507.0789895221.31460082201494e-06
Epanechnikov328342.2970331751.29449452062447e-06
Rectangular359471.5376313941.34213057448622e-06
Triangular331801.1015440881.29527952960527e-06
Biweight331801.1015440881.30046322167624e-06
Cosine328342.2970331751.3019691860606e-06
Optcosine338718.7105659141.29450426197957e-06


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; 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):
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')
}