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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 27 Oct 2016 19:29:13 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/27/t147758937104158jyqoewnodq.htm/, Retrieved Thu, 07 Jul 2022 14:35:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296689, Retrieved Thu, 07 Jul 2022 14:35:00 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [] [2016-10-27 17:29:13] [67fe698233d7575d27222b521501ef35] [Current]
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Dataseries X:
2.132
1.964
2.209
1.965
2.631
2.583
2.714
2.248
2.364
3.042
2.316
2.735
2.493
2.136
2.467
2.414
2.556
2.768
2.998
2.573
3.005
3.469
2.540
3.187
2.689
2.154
3.065
2.397
2.787
3.579
2.915
3.025
3.245
3.328
2.840
3.342
2.261
2.590
2.624
1.860
2.577
2.646
2.639
2.807
2.350
3.053
2.203
2.471
1.967
2.473
2.397
1.904
2.732
2.297
2.734
2.719
2.296
3.243
2.166
2.261
2.408
2.536
2.324
2.178
2.803
2.604
2.782
2.656
2.801
3.122
2.393
2.233
2.451
2.596
2.467
2.210
2.948
2.507
3.019
2.401
2.818
3.305
2.101
2.582
2.407
2.416
2.463
2.228
2.616
2.934
2.668
2.808
2.664
3.112
2.321
2.718
2.297
2.534
2.647
2.064
2.642
2.702
2.348
2.734
2.709
3.206
2.214
2.531
2.119
2.369
2.682
1.840
2.622
2.570
2.447
2.871
2.485
2.957
2.102
2.250
2.051
2.260
2.327
1.781
2.631
2.180
2.150
2.837
1.976
2.836
2.203
1.770




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296689&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=296689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296689&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Properties of Density Trace
Bandwidth0.122487720990585
#Observations132

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.122487720990585 \tabularnewline
#Observations & 132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296689&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.122487720990585[/C][/ROW]
[ROW][C]#Observations[/C][C]132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296689&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth0.122487720990585
#Observations132







Maximum Density Values
Kernelx-valuemax. density
Gaussian2.597335894222851.05583313403816
Epanechnikov2.582400906007921.0534868160161
Rectangular2.527639282553161.08491945381148
Triangular2.582400906007921.05807521303045
Biweight2.582400906007921.05272039435713
Cosine2.582400906007921.05241446323582
Optcosine2.577422576602941.05342651470245

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 2.59733589422285 & 1.05583313403816 \tabularnewline
Epanechnikov & 2.58240090600792 & 1.0534868160161 \tabularnewline
Rectangular & 2.52763928255316 & 1.08491945381148 \tabularnewline
Triangular & 2.58240090600792 & 1.05807521303045 \tabularnewline
Biweight & 2.58240090600792 & 1.05272039435713 \tabularnewline
Cosine & 2.58240090600792 & 1.05241446323582 \tabularnewline
Optcosine & 2.57742257660294 & 1.05342651470245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296689&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]2.59733589422285[/C][C]1.05583313403816[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]2.58240090600792[/C][C]1.0534868160161[/C][/ROW]
[ROW][C]Rectangular[/C][C]2.52763928255316[/C][C]1.08491945381148[/C][/ROW]
[ROW][C]Triangular[/C][C]2.58240090600792[/C][C]1.05807521303045[/C][/ROW]
[ROW][C]Biweight[/C][C]2.58240090600792[/C][C]1.05272039435713[/C][/ROW]
[ROW][C]Cosine[/C][C]2.58240090600792[/C][C]1.05241446323582[/C][/ROW]
[ROW][C]Optcosine[/C][C]2.57742257660294[/C][C]1.05342651470245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296689&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian2.597335894222851.05583313403816
Epanechnikov2.582400906007921.0534868160161
Rectangular2.527639282553161.08491945381148
Triangular2.582400906007921.05807521303045
Biweight2.582400906007921.05272039435713
Cosine2.582400906007921.05241446323582
Optcosine2.577422576602941.05342651470245







Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown

\begin{tabular}{lllllllll}
\hline
Kernel Density Values \tabularnewline
x-value & Gaussian & Epanechnikov & Rectangular & Triangular & Biweight & Cosine & Optcosine \tabularnewline
Kernel Density Values are not shown \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296689&T=3

[TABLE]
[ROW][C]Kernel Density Values[/C][/ROW]
[ROW][C]x-value[/C][C]Gaussian[/C][C]Epanechnikov[/C][C]Rectangular[/C][C]Triangular[/C][C]Biweight[/C][C]Cosine[/C][C]Optcosine[/C][/ROW]
[ROW][C]Kernel Density Values are not shown[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296689&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296689&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown



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')
ab<-table.start()
ab<-table.row.start(ab)
ab<-table.element(ab,'Properties of Density Trace',2,TRUE)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'Bandwidth',header=TRUE)
ab<-table.element(ab,mydensity1$bw)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'#Observations',header=TRUE)
ab<-table.element(ab,mydensity1$n)
ab<-table.row.end(ab)
ab<-table.end(ab)
a <- ab
table.save(ab,file='mytable123.tab')
b<-table.start()
b<-table.row.start(b)
b<-table.element(b,'Maximum Density Values',3,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Kernel',1,TRUE)
b<-table.element(b,'x-value',1,TRUE)
b<-table.element(b,'max. density',1,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Gaussian',1,TRUE)
b<-table.element(b,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
b<-table.element(b,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Epanechnikov',1,TRUE)
b<-table.element(b,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
b<-table.element(b,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Rectangular',1,TRUE)
b<-table.element(b,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
b<-table.element(b,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Triangular',1,TRUE)
b<-table.element(b,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
b<-table.element(b,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Biweight',1,TRUE)
b<-table.element(b,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
b<-table.element(b,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Cosine',1,TRUE)
b<-table.element(b,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
b<-table.element(b,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Optcosine',1,TRUE)
b<-table.element(b,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
b<-table.element(b,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
b<-table.row.end(b)
b<-table.end(b)
a <- b[1]
table.save(b,file='mytable2a.tab')
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)
if (par2=='yes') {
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)
}
} else {
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values are not shown',8)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')