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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 computationThu, 18 Dec 2014 13:51:14 +0000
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/Dec/18/t14189106885ugzzqmv25w18ic.htm/, Retrieved Sun, 19 May 2024 18:22:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270932, Retrieved Sun, 19 May 2024 18:22:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [Bachelor 2012] [2014-12-18 13:51:14] [f02c6c9412fee5ce04bac553459224aa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
52
55
72
33
66
66
64
40
46
58
51
50
52
54
66
61
80
51
56
53
47
50
39
58
35
58
60
62
63
53
46
67
59
64
38
50
48
47
66
63
44
43
38
56
45
50
54
55
37
46
51
64
47
62
67
56
65
50
57
47
47
57
50
22
59
56
53
42
52
54
44
62
53
50
36
76
66
62
59
47
55
58
60
57

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270932&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270932&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth3.66857778722549
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 3.66857778722549 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270932&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]3.66857778722549[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270932&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
Bandwidth3.66857778722549
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular52.01775838297810.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.4269622978708 & 0.0392242030319183 \tabularnewline
Epanechnikov & 52.8006494468074 & 0.0393976851248004 \tabularnewline
Rectangular & 52.0177583829781 & 0.0412178216076804 \tabularnewline
Triangular & 52.9572276595732 & 0.0391249951163551 \tabularnewline
Biweight & 53.1138058723391 & 0.0391823603103853 \tabularnewline
Cosine & 53.2703840851049 & 0.0391817674686529 \tabularnewline
Optcosine & 52.8006494468074 & 0.0393057515828613 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270932&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]53.4269622978708[/C][C]0.0392242030319183[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]52.8006494468074[/C][C]0.0393976851248004[/C][/ROW]
[ROW][C]Rectangular[/C][C]52.0177583829781[/C][C]0.0412178216076804[/C][/ROW]
[ROW][C]Triangular[/C][C]52.9572276595732[/C][C]0.0391249951163551[/C][/ROW]
[ROW][C]Biweight[/C][C]53.1138058723391[/C][C]0.0391823603103853[/C][/ROW]
[ROW][C]Cosine[/C][C]53.2703840851049[/C][C]0.0391817674686529[/C][/ROW]
[ROW][C]Optcosine[/C][C]52.8006494468074[/C][C]0.0393057515828613[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270932&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
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular52.01775838297810.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular52.17433659574390.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.4269622978708 & 0.0392242030319183 \tabularnewline
Epanechnikov & 52.8006494468074 & 0.0393976851248004 \tabularnewline
Rectangular & 52.1743365957439 & 0.0412178216076804 \tabularnewline
Triangular & 52.9572276595732 & 0.0391249951163551 \tabularnewline
Biweight & 53.1138058723391 & 0.0391823603103853 \tabularnewline
Cosine & 53.2703840851049 & 0.0391817674686529 \tabularnewline
Optcosine & 52.8006494468074 & 0.0393057515828613 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270932&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]53.4269622978708[/C][C]0.0392242030319183[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]52.8006494468074[/C][C]0.0393976851248004[/C][/ROW]
[ROW][C]Rectangular[/C][C]52.1743365957439[/C][C]0.0412178216076804[/C][/ROW]
[ROW][C]Triangular[/C][C]52.9572276595732[/C][C]0.0391249951163551[/C][/ROW]
[ROW][C]Biweight[/C][C]53.1138058723391[/C][C]0.0391823603103853[/C][/ROW]
[ROW][C]Cosine[/C][C]53.2703840851049[/C][C]0.0391817674686529[/C][/ROW]
[ROW][C]Optcosine[/C][C]52.8006494468074[/C][C]0.0393057515828613[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270932&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
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular52.17433659574390.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613






Maximum Density Values
Kernelx-valuemax. density
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular55.93221370212450.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 53.4269622978708 & 0.0392242030319183 \tabularnewline
Epanechnikov & 52.8006494468074 & 0.0393976851248004 \tabularnewline
Rectangular & 55.9322137021245 & 0.0412178216076804 \tabularnewline
Triangular & 52.9572276595732 & 0.0391249951163551 \tabularnewline
Biweight & 53.1138058723391 & 0.0391823603103853 \tabularnewline
Cosine & 53.2703840851049 & 0.0391817674686529 \tabularnewline
Optcosine & 52.8006494468074 & 0.0393057515828613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270932&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]53.4269622978708[/C][C]0.0392242030319183[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]52.8006494468074[/C][C]0.0393976851248004[/C][/ROW]
[ROW][C]Rectangular[/C][C]55.9322137021245[/C][C]0.0412178216076804[/C][/ROW]
[ROW][C]Triangular[/C][C]52.9572276595732[/C][C]0.0391249951163551[/C][/ROW]
[ROW][C]Biweight[/C][C]53.1138058723391[/C][C]0.0391823603103853[/C][/ROW]
[ROW][C]Cosine[/C][C]53.2703840851049[/C][C]0.0391817674686529[/C][/ROW]
[ROW][C]Optcosine[/C][C]52.8006494468074[/C][C]0.0393057515828613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270932&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270932&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
Gaussian53.42696229787080.0392242030319183
Epanechnikov52.80064944680740.0393976851248004
Rectangular55.93221370212450.0412178216076804
Triangular52.95722765957320.0391249951163551
Biweight53.11380587233910.0391823603103853
Cosine53.27038408510490.0391817674686529
Optcosine52.80064944680740.0393057515828613


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')
}