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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 computationMon, 15 Dec 2014 15:11:16 +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/15/t14186562924y49m0h55ugjayv.htm/, Retrieved Thu, 16 May 2024 23:25:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268604, Retrieved Thu, 16 May 2024 23:25:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Maximum-likelihood Fitting - Normal Distribution] [Intrinsic Motivat...] [2010-10-12 11:57:21] [b98453cac15ba1066b407e146608df68]
- RMP   [Maximum-likelihood Fitting - Normal Distribution] [] [2014-10-14 18:01:50] [32b17a345b130fdf5cc88718ed94a974]
- RMPD      [Kernel Density Estimation] [Gaussian AM] [2014-12-15 15:11:16] [9636d26fd774798d33054b538c301d75] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4
9
4
5
4
4
9
8
11
4
4
6
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8
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11
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10
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7
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4
4
4
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10
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4
7
4
8
11
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14
5
4
8
9
4
4
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4
5
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4
7
10
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4
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5
4
17
4
4
8
4
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4
4
5
7
4
4
7
11
7
4
4
4
4
4
4
6
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23
4
8
6
4
4
7
4
4
4
4
10
6
5
5
4
4
5
5
5
5
4
6
4
4
4
9
18
6
5
4
11
4
10
6
8
8
6
8
4
4
9
9
5
4
4
15
10
9
7
9
6
4
7
4
7
4
15
4
9
4
4
28
4
4
4
5
4
4
12
5
4
6
6
5
4
4
4
10
7
4
4
7
4
4
12
5
8
6
17
4
5
4
5
5
6
4
4
4
6
8
10
4
5
4
4
4
16
4
7
4
4
14
5
5
5
5
7
19
16
4
4
7
9
5
14
4
16
10
5
6
4
4
4
5
4
4
5
4
4
5
8
15

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268604&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268604&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268604&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 time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth0.650108372467663
#Observations286

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.650108372467663 \tabularnewline
#Observations & 286 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268604&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.650108372467663[/C][/ROW]
[ROW][C]#Observations[/C][C]286[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268604&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268604&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
Bandwidth0.650108372467663
#Observations286






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.124478618257730.316438784706448
Epanechnikov4.233678814871450.286141399023068
Rectangular4.998080191167510.299650422023007
Triangular4.015278421644010.321050124318875
Biweight4.179078716564590.294089936374074
Cosine4.179078716564590.297192724510951
Optcosine4.179078716564590.288518866065562

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.12447861825773 & 0.316438784706448 \tabularnewline
Epanechnikov & 4.23367881487145 & 0.286141399023068 \tabularnewline
Rectangular & 4.99808019116751 & 0.299650422023007 \tabularnewline
Triangular & 4.01527842164401 & 0.321050124318875 \tabularnewline
Biweight & 4.17907871656459 & 0.294089936374074 \tabularnewline
Cosine & 4.17907871656459 & 0.297192724510951 \tabularnewline
Optcosine & 4.17907871656459 & 0.288518866065562 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268604&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]4.12447861825773[/C][C]0.316438784706448[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.23367881487145[/C][C]0.286141399023068[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.99808019116751[/C][C]0.299650422023007[/C][/ROW]
[ROW][C]Triangular[/C][C]4.01527842164401[/C][C]0.321050124318875[/C][/ROW]
[ROW][C]Biweight[/C][C]4.17907871656459[/C][C]0.294089936374074[/C][/ROW]
[ROW][C]Cosine[/C][C]4.17907871656459[/C][C]0.297192724510951[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.17907871656459[/C][C]0.288518866065562[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268604&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268604&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
Gaussian4.124478618257730.316438784706448
Epanechnikov4.233678814871450.286141399023068
Rectangular4.998080191167510.299650422023007
Triangular4.015278421644010.321050124318875
Biweight4.179078716564590.294089936374074
Cosine4.179078716564590.297192724510951
Optcosine4.179078716564590.288518866065562






Maximum Density Values
Kernelx-valuemax. density
Gaussian4.124478618257730.316438784706448
Epanechnikov4.233678814871450.286141399023068
Rectangular5.052680289474370.299650422023007
Triangular4.015278421644010.321050124318875
Biweight4.179078716564590.294089936374074
Cosine4.179078716564590.297192724510951
Optcosine4.179078716564590.288518866065562

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.12447861825773 & 0.316438784706448 \tabularnewline
Epanechnikov & 4.23367881487145 & 0.286141399023068 \tabularnewline
Rectangular & 5.05268028947437 & 0.299650422023007 \tabularnewline
Triangular & 4.01527842164401 & 0.321050124318875 \tabularnewline
Biweight & 4.17907871656459 & 0.294089936374074 \tabularnewline
Cosine & 4.17907871656459 & 0.297192724510951 \tabularnewline
Optcosine & 4.17907871656459 & 0.288518866065562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268604&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]4.12447861825773[/C][C]0.316438784706448[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.23367881487145[/C][C]0.286141399023068[/C][/ROW]
[ROW][C]Rectangular[/C][C]5.05268028947437[/C][C]0.299650422023007[/C][/ROW]
[ROW][C]Triangular[/C][C]4.01527842164401[/C][C]0.321050124318875[/C][/ROW]
[ROW][C]Biweight[/C][C]4.17907871656459[/C][C]0.294089936374074[/C][/ROW]
[ROW][C]Cosine[/C][C]4.17907871656459[/C][C]0.297192724510951[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.17907871656459[/C][C]0.288518866065562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268604&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268604&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
Gaussian4.124478618257730.316438784706448
Epanechnikov4.233678814871450.286141399023068
Rectangular5.052680289474370.299650422023007
Triangular4.015278421644010.321050124318875
Biweight4.179078716564590.294089936374074
Cosine4.179078716564590.297192724510951
Optcosine4.179078716564590.288518866065562


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
}