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Description of Statistical Computation

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 computationSun, 30 Aug 2015 16:50:03 +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/2015/Aug/30/t1440949900xt4ipvi8zuka3iu.htm/, Retrieved Thu, 31 Oct 2024 23:00:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280369, Retrieved Thu, 31 Oct 2024 23:00:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Skewness and Kurtosis Test] [Skewness test] [2015-01-14 08:02:04] [46c7ebd23dbdec306a09830d8b7528e7]
- RMPD    [Kernel Density Estimation] [] [2015-08-30 15:50:03] [bcb5b2244e18c223160d6809eb45aeed] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21
22
22
18
23
12
20
22
21
19
22
15
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19
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21
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21
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25
9
30
20
23
16
16
19
25
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21
10
14
22
26
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24
18
23
15
19
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27
21
13
8
29
28
23
21
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25
19
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14
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20
12
24
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12
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10
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17
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18
21
20
20
22
19
20
26
23
24
21
21
19
8
17
20
11
8
15
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18
19
19
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21
25
30
17
27
23
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18
23
19
15
20
16
24
25
25
19
19
16
19
19
23
21
22
19
20
20
3
23
23
20
15
16
7
24
17
24
24
19
25
20
28
23
27
18
28
21
19
23
27
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28
25
21
22
28
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29
25
25
20
20
16
20
20
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18
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18
19
25
25
25
24
19
26
10
17
13
17
30
25
4
16
21
23
22
17
20
20
22
16
23
0
18
25
23
12
18
24
11
18
23
24
29
18
15
29
16
19
22
16
23
23
19
4
20
24
20
4
24
22
16
3
15
24
17
20
27
26
23
17
20
22
19
24
19
23
15
27
26
22
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18
15
22
27
10
20
17
23
19
13
27
23
16
25
2
26
20
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24

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280369&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280369&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'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth1.089679438726
#Observations278

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.089679438726 \tabularnewline
#Observations & 278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280369&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.089679438726[/C][/ROW]
[ROW][C]#Observations[/C][C]278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280369&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
Bandwidth1.089679438726
#Observations278






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.18501688590760.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5404459220247 & 0.0914040120002995 \tabularnewline
Epanechnikov & 19.969464434342 & 0.0900511815099038 \tabularnewline
Rectangular & 21.1850168859076 & 0.0971999399440316 \tabularnewline
Triangular & 19.969464434342 & 0.0920662985547164 \tabularnewline
Biweight & 19.6834520927971 & 0.0896326679330326 \tabularnewline
Cosine & 19.6119490074109 & 0.0899465464928877 \tabularnewline
Optcosine & 19.8979613489557 & 0.0899752480004639 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280369&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]19.5404459220247[/C][C]0.0914040120002995[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.969464434342[/C][C]0.0900511815099038[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.1850168859076[/C][C]0.0971999399440316[/C][/ROW]
[ROW][C]Triangular[/C][C]19.969464434342[/C][C]0.0920662985547164[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6834520927971[/C][C]0.0896326679330326[/C][/ROW]
[ROW][C]Cosine[/C][C]19.6119490074109[/C][C]0.0899465464928877[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8979613489557[/C][C]0.0899752480004639[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280369&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280369&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
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.18501688590760.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.25651997129380.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5404459220247 & 0.0914040120002995 \tabularnewline
Epanechnikov & 19.969464434342 & 0.0900511815099038 \tabularnewline
Rectangular & 21.2565199712938 & 0.0971999399440316 \tabularnewline
Triangular & 19.969464434342 & 0.0920662985547164 \tabularnewline
Biweight & 19.6834520927971 & 0.0896326679330326 \tabularnewline
Cosine & 19.6119490074109 & 0.0899465464928877 \tabularnewline
Optcosine & 19.8979613489557 & 0.0899752480004639 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280369&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]19.5404459220247[/C][C]0.0914040120002995[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.969464434342[/C][C]0.0900511815099038[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.2565199712938[/C][C]0.0971999399440316[/C][/ROW]
[ROW][C]Triangular[/C][C]19.969464434342[/C][C]0.0920662985547164[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6834520927971[/C][C]0.0896326679330326[/C][/ROW]
[ROW][C]Cosine[/C][C]19.6119490074109[/C][C]0.0899465464928877[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8979613489557[/C][C]0.0899752480004639[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280369&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280369&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
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.25651997129380.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639






Maximum Density Values
Kernelx-valuemax. density
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.328023056680.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19.5404459220247 & 0.0914040120002995 \tabularnewline
Epanechnikov & 19.969464434342 & 0.0900511815099038 \tabularnewline
Rectangular & 21.32802305668 & 0.0971999399440316 \tabularnewline
Triangular & 19.969464434342 & 0.0920662985547164 \tabularnewline
Biweight & 19.6834520927971 & 0.0896326679330326 \tabularnewline
Cosine & 19.6119490074109 & 0.0899465464928877 \tabularnewline
Optcosine & 19.8979613489557 & 0.0899752480004639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280369&T=4

[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]19.5404459220247[/C][C]0.0914040120002995[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]19.969464434342[/C][C]0.0900511815099038[/C][/ROW]
[ROW][C]Rectangular[/C][C]21.32802305668[/C][C]0.0971999399440316[/C][/ROW]
[ROW][C]Triangular[/C][C]19.969464434342[/C][C]0.0920662985547164[/C][/ROW]
[ROW][C]Biweight[/C][C]19.6834520927971[/C][C]0.0896326679330326[/C][/ROW]
[ROW][C]Cosine[/C][C]19.6119490074109[/C][C]0.0899465464928877[/C][/ROW]
[ROW][C]Optcosine[/C][C]19.8979613489557[/C][C]0.0899752480004639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280369&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280369&T=4

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
Gaussian19.54044592202470.0914040120002995
Epanechnikov19.9694644343420.0900511815099038
Rectangular21.328023056680.0971999399440316
Triangular19.9694644343420.0920662985547164
Biweight19.68345209279710.0896326679330326
Cosine19.61194900741090.0899465464928877
Optcosine19.89796134895570.0899752480004639


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')
}