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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 computationTue, 19 Dec 2017 13:03:03 +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/2017/Dec/19/t15136850678tpj2i3m23ob6f1.htm/, Retrieved Wed, 15 May 2024 07:22:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310314, Retrieved Wed, 15 May 2024 07:22:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [Dataset 1: Kernel...] [2017-12-19 12:03:03] [d2f3f1c36efc482093437f9590ab82ed] [Current]
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Dataseries X:
7
8
10
10
5
7
8
9
8
8
8
10
10
8
10
9
7
8
10
4
9
5
4
9
6
8
10
9
8
7
10
6
9
5
4
8
2
10
5
8
8
8
7
10
10
7
10
10
8
7
8
6
10
9
9
7
8
6
7
9
7
7
7
10
4
10
3
8
10
8
6
6
10
10
7
8
7
9
2
10
10
7
8
8
10
8
8
7
8
8
10
9
9
4
5
10
9
6
8
8
9
8
4
5
10
10
9
9
6
7
4
6
4
4
10
6
9
7
4
8
8
8
7
6
5
5
7
4
8
7
6
8
5
3
5
10
7
4
2
6
3
8
9
5
6
2
6
10
8
10
8
8
6
9
9
9
8
8
10
3
6
9
3
4
5
9
8
5
4
5
7
7
8
8
6
7
9
9
6
9
9
8
6
6
10
8
10
8
7
7
8
8
7
2
5
7
5
5
10
8
7
6
6
5
7
8
7
8
9
5
5
5
10
5
5
8
10
7
2
6
3
6
4
4
8
7
5
9
5
6
5
2
8
7
9
9
9
10
6
9
9
6
10
5
9
4
2
3
9
10
6
9
8
2
6
9
6
4
3
3
4
6
8
6
7
8
3
10
8
6
10
8
10
7
10
6
7
9
6
7
6
4
6
8
9
8
6
6
10
8
8
7
4
9
8
10
8
6
7
8
5
10
2
6
7
5
8
7
7
10
7
6
10
6
5
8
8
5
8
10
7
7
7
7
2
4
6
7
9
9
4
9
9
8
7
9
7
6
7
2
3
4
5
2
6
8
5
4
10
10
10
9
5
5
7
10
9
8
8
8
8
8
7
6
8
2
5
4
9
10
6
4
10
6
7
7
8
6
5
6
7
6
9
9
7
6
7
7
8
7
8
7
4
10
8
8
2
6
4
4
9
2
6
7
4
10
3
7
4
8
4
5
6
5
9
6
8
4
4
8
4
10
8
5
3
7
6
5
5
9
2
7
7
5
9
4
5
9
7
6
8
7
6
8
6
7




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=310314&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=310314&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310314&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
Bandwidth0.568407725893399
#Observations446

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.568407725893399 \tabularnewline
#Observations & 446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310314&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.568407725893399[/C][/ROW]
[ROW][C]#Observations[/C][C]446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310314&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310314&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
Bandwidth0.568407725893399
#Observations446







Maximum Density Values
Kernelx-valuemax. density
Gaussian7.886854632148640.182401944535345
Epanechnikov7.931513913382920.181421183249074
Rectangular7.239295054251470.181055478397942
Triangular7.998502835234350.197921597317305
Biweight7.819865710297210.180203709207158
Cosine7.819865710297210.180461642779028
Optcosine7.909184272765780.181376482483412

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 7.88685463214864 & 0.182401944535345 \tabularnewline
Epanechnikov & 7.93151391338292 & 0.181421183249074 \tabularnewline
Rectangular & 7.23929505425147 & 0.181055478397942 \tabularnewline
Triangular & 7.99850283523435 & 0.197921597317305 \tabularnewline
Biweight & 7.81986571029721 & 0.180203709207158 \tabularnewline
Cosine & 7.81986571029721 & 0.180461642779028 \tabularnewline
Optcosine & 7.90918427276578 & 0.181376482483412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310314&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]7.88685463214864[/C][C]0.182401944535345[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]7.93151391338292[/C][C]0.181421183249074[/C][/ROW]
[ROW][C]Rectangular[/C][C]7.23929505425147[/C][C]0.181055478397942[/C][/ROW]
[ROW][C]Triangular[/C][C]7.99850283523435[/C][C]0.197921597317305[/C][/ROW]
[ROW][C]Biweight[/C][C]7.81986571029721[/C][C]0.180203709207158[/C][/ROW]
[ROW][C]Cosine[/C][C]7.81986571029721[/C][C]0.180461642779028[/C][/ROW]
[ROW][C]Optcosine[/C][C]7.90918427276578[/C][C]0.181376482483412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310314&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310314&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
Gaussian7.886854632148640.182401944535345
Epanechnikov7.931513913382920.181421183249074
Rectangular7.239295054251470.181055478397942
Triangular7.998502835234350.197921597317305
Biweight7.819865710297210.180203709207158
Cosine7.819865710297210.180461642779028
Optcosine7.909184272765780.181376482483412







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=310314&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=310314&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310314&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):
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')
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')