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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Mon, 11 Dec 2017 15:41:27 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/11/t15130033005h68sxufrp0xqo1.htm/, Retrieved Thu, 16 May 2024 01:57:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309006, Retrieved Thu, 16 May 2024 01:57:32 +0000

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No (this computation is public)

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Estimated Impact

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

-       [Kernel Density Estimation] [Kernel Density Es...] [2017-12-11 14:41:27] [b96fd9fc55b2111e8fcab34a88822fe0] [Current]

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Dataseries X:

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Histogram

Boxplots

0,70
0,91
0,81
0,58
0,51
0,36
0,11
0,77
0,49
0,44
0,54
0,35
0,60
0,52
0,73
0,66
0,79
0,44
0,89
0,74
0,61
0,20
0,77
0,62
0,71
0,10
0,06
0,10
0,63
0,17
0,77
0,72
0,65
0,83
0,61
0,10
0,32
0,20
0,30
0,07
0,29
0,61
0,35
0,31
0,05
0,11
0,06
0,12
0,44
0,63
0,31
0,30
0,67
0,36
0,05
0,18
0,16
0,46
0,57
0,18
0,95
0,25
0,10
0,24

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309006&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309006&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309006&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Properties of Density Trace
Bandwidth	0.103138083278474
#Observations	64

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.103138083278474 \tabularnewline
#Observations & 64 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309006&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.103138083278474[/C][/ROW]
[ROW][C]#Observations[/C][C]64[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309006&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309006&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
Bandwidth	0.103138083278474
#Observations	64

Maximum Density Values
Kernel	x-value	max. density
Gaussian	0.641182688325568	1.20990343245447
Epanechnikov	0.195342619929038	1.2064078295949
Rectangular	0.189398085683751	1.31199325254051
Triangular	0.629293619834994	1.20492108111168
Biweight	0.204259421296969	1.19397325572362
Cosine	0.644154955448211	1.19184581573121
Optcosine	0.213176222664899	1.19896355761397

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.641182688325568 & 1.20990343245447 \tabularnewline
Epanechnikov & 0.195342619929038 & 1.2064078295949 \tabularnewline
Rectangular & 0.189398085683751 & 1.31199325254051 \tabularnewline
Triangular & 0.629293619834994 & 1.20492108111168 \tabularnewline
Biweight & 0.204259421296969 & 1.19397325572362 \tabularnewline
Cosine & 0.644154955448211 & 1.19184581573121 \tabularnewline
Optcosine & 0.213176222664899 & 1.19896355761397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309006&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]0.641182688325568[/C][C]1.20990343245447[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.195342619929038[/C][C]1.2064078295949[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.189398085683751[/C][C]1.31199325254051[/C][/ROW]
[ROW][C]Triangular[/C][C]0.629293619834994[/C][C]1.20492108111168[/C][/ROW]
[ROW][C]Biweight[/C][C]0.204259421296969[/C][C]1.19397325572362[/C][/ROW]
[ROW][C]Cosine[/C][C]0.644154955448211[/C][C]1.19184581573121[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.213176222664899[/C][C]1.19896355761397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309006&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309006&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
Kernel	x-value	max. density
Gaussian	0.641182688325568	1.20990343245447
Epanechnikov	0.195342619929038	1.2064078295949
Rectangular	0.189398085683751	1.31199325254051
Triangular	0.629293619834994	1.20492108111168
Biweight	0.204259421296969	1.19397325572362
Cosine	0.644154955448211	1.19184581573121
Optcosine	0.213176222664899	1.19896355761397

Kernel Density Values
x-value	Gaussian	Epanechnikov	Rectangular	Triangular	Biweight	Cosine	Optcosine
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=309006&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=309006&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309006&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-value	Gaussian	Epanechnikov	Rectangular	Triangular	Biweight	Cosine	Optcosine
Kernel Density Values are not shown

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Figure 4

PNG link

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PDF link

Figure 5

PNG link

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PDF link

Figure 6

PNG link

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PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code