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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 26 Sep 2013 09:12:27 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Sep/26/t1380201189svzk6k6qp1meui8.htm/, Retrieved Mon, 29 Apr 2024 10:22:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212104, Retrieved Mon, 29 Apr 2024 10:22:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2013-09-18 16:04:34] [286671ed39c318cd0dd94a3fd3744eb8]
- RMPD    [Kernel Density Estimation] [] [2013-09-26 13:12:27] [764249a9cc4864d99a8b0ce95556daaa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99.42
99.42
99.42
99.42
99.42
109.26
110
110
109.26
100.07
100.07
100.05
100.05
100.05
100.05
100.05
100.05
108.77
111.32
111.6
108.52
103.13
102.87
102.75
102.75
102.75
102.75
102.75
102.75
115.22
115.53
115.4
111.99
107.93
107.43
106.98
106.98
106.98
106.98
106.98
106.98
113.71
118.77
118.54
116.16
110.52
110.06
109.9
109.9
110.72
110.09
110.07
112.45
113.06
119.83
119.84
113.73
110.5
110.12
109.86
110.36
110.36
110.59
112.52
112.1
115.9
122.96
121.26
114.55
111.57
110.65
109.77
112.38
112.35
112.2
114.46
116.26
119.57
127.77
126.59
120.45
116.38
116.3
115.05

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212104&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]5 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=212104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212104&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth2.18591861359587
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.18591861359587 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212104&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.18591861359587[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212104&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
Bandwidth2.18591861359587
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian110.633177737030.0698451040876985
Epanechnikov110.7954693678780.0665548446550643
Rectangular112.742968938050.0676027804161895
Triangular110.4708861061830.0691104107703533
Biweight110.7143235524540.0674460113922218
Cosine110.7143235524540.0678466196949841
Optcosine110.7143235524540.0668657690043947

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 110.63317773703 & 0.0698451040876985 \tabularnewline
Epanechnikov & 110.795469367878 & 0.0665548446550643 \tabularnewline
Rectangular & 112.74296893805 & 0.0676027804161895 \tabularnewline
Triangular & 110.470886106183 & 0.0691104107703533 \tabularnewline
Biweight & 110.714323552454 & 0.0674460113922218 \tabularnewline
Cosine & 110.714323552454 & 0.0678466196949841 \tabularnewline
Optcosine & 110.714323552454 & 0.0668657690043947 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212104&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]110.63317773703[/C][C]0.0698451040876985[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]110.795469367878[/C][C]0.0665548446550643[/C][/ROW]
[ROW][C]Rectangular[/C][C]112.74296893805[/C][C]0.0676027804161895[/C][/ROW]
[ROW][C]Triangular[/C][C]110.470886106183[/C][C]0.0691104107703533[/C][/ROW]
[ROW][C]Biweight[/C][C]110.714323552454[/C][C]0.0674460113922218[/C][/ROW]
[ROW][C]Cosine[/C][C]110.714323552454[/C][C]0.0678466196949841[/C][/ROW]
[ROW][C]Optcosine[/C][C]110.714323552454[/C][C]0.0668657690043947[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212104&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
Gaussian110.633177737030.0698451040876985
Epanechnikov110.7954693678780.0665548446550643
Rectangular112.742968938050.0676027804161895
Triangular110.4708861061830.0691104107703533
Biweight110.7143235524540.0674460113922218
Cosine110.7143235524540.0678466196949841
Optcosine110.7143235524540.0668657690043947






Maximum Density Values
Kernelx-valuemax. density
Gaussian110.633177737030.0698451040876985
Epanechnikov110.7954693678780.0665548446550643
Rectangular112.8241147534740.0676027804161895
Triangular110.4708861061830.0691104107703533
Biweight110.7143235524540.0674460113922218
Cosine110.7143235524540.0678466196949841
Optcosine110.7143235524540.0668657690043947

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 110.63317773703 & 0.0698451040876985 \tabularnewline
Epanechnikov & 110.795469367878 & 0.0665548446550643 \tabularnewline
Rectangular & 112.824114753474 & 0.0676027804161895 \tabularnewline
Triangular & 110.470886106183 & 0.0691104107703533 \tabularnewline
Biweight & 110.714323552454 & 0.0674460113922218 \tabularnewline
Cosine & 110.714323552454 & 0.0678466196949841 \tabularnewline
Optcosine & 110.714323552454 & 0.0668657690043947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212104&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]110.63317773703[/C][C]0.0698451040876985[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]110.795469367878[/C][C]0.0665548446550643[/C][/ROW]
[ROW][C]Rectangular[/C][C]112.824114753474[/C][C]0.0676027804161895[/C][/ROW]
[ROW][C]Triangular[/C][C]110.470886106183[/C][C]0.0691104107703533[/C][/ROW]
[ROW][C]Biweight[/C][C]110.714323552454[/C][C]0.0674460113922218[/C][/ROW]
[ROW][C]Cosine[/C][C]110.714323552454[/C][C]0.0678466196949841[/C][/ROW]
[ROW][C]Optcosine[/C][C]110.714323552454[/C][C]0.0668657690043947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212104&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
Gaussian110.633177737030.0698451040876985
Epanechnikov110.7954693678780.0665548446550643
Rectangular112.8241147534740.0676027804161895
Triangular110.4708861061830.0691104107703533
Biweight110.7143235524540.0674460113922218
Cosine110.7143235524540.0678466196949841
Optcosine110.7143235524540.0668657690043947


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')
}