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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, 21 May 2015 15:32:07 +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/May/21/t14322189109yxzvmrusmzx693.htm/, Retrieved Sat, 04 May 2024 19:19:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279191, Retrieved Sat, 04 May 2024 19:19:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [] [2015-02-09 09:38:39] [1f4ce71c1a7ae502d60225fda197c28f]
- RMPD    [Kernel Density Estimation] [] [2015-05-21 14:32:07] [c6da619eabbd864125b02146bc2bbd84] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.5469
1.5501
1.5494
1.5475
1.5449
1.5391
1.5578
1.5528
1.5496
1.549
1.5449
1.5479
1.5494
1.558
1.5691
1.5748
1.5564
1.5601
1.5687
1.5775
1.5841
1.5898
1.5922
1.5969
1.6155
1.6212
1.6124
1.6375
1.6506
1.6543
1.6567
1.6383
1.6475
1.6706
1.6485
1.6592
1.6203
1.608
1.572
1.5964
1.6247
1.6139
1.6193
1.6212
1.5942
1.5194
1.5162
1.5393
1.4935
1.4904
1.5083
1.5147
1.5118
1.5148
1.5202
1.5236
1.5148
1.5138
1.5105
1.502
1.4765
1.4671
1.4482
1.4337
1.4181
1.3767
1.346
1.3413
1.3089
1.3452
1.3442
1.2811
1.2779
1.2974
1.2867
1.2977
1.2537
1.2092
1.1766
1.1203
1.2005
1.2295
1.2307
1.2276
1.2108
1.2071
1.2061
1.2023
1.2012
1.2011
1.2011
1.2011
1.2089
1.2098
1.2052
1.2091
1.2288
1.2298
1.2266
1.2199
1.2418
1.2322
1.2366
1.2338
1.2338
1.2316
1.2316
1.2245

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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&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 Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth0.0590756039872133
#Observations108

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0590756039872133 \tabularnewline
#Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0590756039872133[/C][/ROW]
[ROW][C]#Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&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
Bandwidth0.0590756039872133
#Observations108






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.562767450999512.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.56099689596248 & 2.87648924245068 \tabularnewline
Epanechnikov & 1.56630856107357 & 2.78428687538641 \tabularnewline
Rectangular & 1.56276745099951 & 2.75998858552682 \tabularnewline
Triangular & 1.55568523085138 & 2.83229240081523 \tabularnewline
Biweight & 1.56453800603654 & 2.80895275008944 \tabularnewline
Cosine & 1.56453800603654 & 2.81793360268617 \tabularnewline
Optcosine & 1.56453800603654 & 2.79096083066781 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&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]1.56099689596248[/C][C]2.87648924245068[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.56630856107357[/C][C]2.78428687538641[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.56276745099951[/C][C]2.75998858552682[/C][/ROW]
[ROW][C]Triangular[/C][C]1.55568523085138[/C][C]2.83229240081523[/C][/ROW]
[ROW][C]Biweight[/C][C]1.56453800603654[/C][C]2.80895275008944[/C][/ROW]
[ROW][C]Cosine[/C][C]1.56453800603654[/C][C]2.81793360268617[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.56453800603654[/C][C]2.79096083066781[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&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
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.562767450999512.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.564538006036542.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.56099689596248 & 2.87648924245068 \tabularnewline
Epanechnikov & 1.56630856107357 & 2.78428687538641 \tabularnewline
Rectangular & 1.56453800603654 & 2.75998858552682 \tabularnewline
Triangular & 1.55568523085138 & 2.83229240081523 \tabularnewline
Biweight & 1.56453800603654 & 2.80895275008944 \tabularnewline
Cosine & 1.56453800603654 & 2.81793360268617 \tabularnewline
Optcosine & 1.56453800603654 & 2.79096083066781 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&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]1.56099689596248[/C][C]2.87648924245068[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.56630856107357[/C][C]2.78428687538641[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.56453800603654[/C][C]2.75998858552682[/C][/ROW]
[ROW][C]Triangular[/C][C]1.55568523085138[/C][C]2.83229240081523[/C][/ROW]
[ROW][C]Biweight[/C][C]1.56453800603654[/C][C]2.80895275008944[/C][/ROW]
[ROW][C]Cosine[/C][C]1.56453800603654[/C][C]2.81793360268617[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.56453800603654[/C][C]2.79096083066781[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&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
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.564538006036542.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.566308561073572.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.56099689596248 & 2.87648924245068 \tabularnewline
Epanechnikov & 1.56630856107357 & 2.78428687538641 \tabularnewline
Rectangular & 1.56630856107357 & 2.75998858552682 \tabularnewline
Triangular & 1.55568523085138 & 2.83229240081523 \tabularnewline
Biweight & 1.56453800603654 & 2.80895275008944 \tabularnewline
Cosine & 1.56453800603654 & 2.81793360268617 \tabularnewline
Optcosine & 1.56453800603654 & 2.79096083066781 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&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]1.56099689596248[/C][C]2.87648924245068[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.56630856107357[/C][C]2.78428687538641[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.56630856107357[/C][C]2.75998858552682[/C][/ROW]
[ROW][C]Triangular[/C][C]1.55568523085138[/C][C]2.83229240081523[/C][/ROW]
[ROW][C]Biweight[/C][C]1.56453800603654[/C][C]2.80895275008944[/C][/ROW]
[ROW][C]Cosine[/C][C]1.56453800603654[/C][C]2.81793360268617[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.56453800603654[/C][C]2.79096083066781[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&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
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.566308561073572.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781






Maximum Density Values
Kernelx-valuemax. density
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.57339078122172.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1.56099689596248 & 2.87648924245068 \tabularnewline
Epanechnikov & 1.56630856107357 & 2.78428687538641 \tabularnewline
Rectangular & 1.5733907812217 & 2.75998858552682 \tabularnewline
Triangular & 1.55568523085138 & 2.83229240081523 \tabularnewline
Biweight & 1.56453800603654 & 2.80895275008944 \tabularnewline
Cosine & 1.56453800603654 & 2.81793360268617 \tabularnewline
Optcosine & 1.56453800603654 & 2.79096083066781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279191&T=5

[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]1.56099689596248[/C][C]2.87648924245068[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.56630856107357[/C][C]2.78428687538641[/C][/ROW]
[ROW][C]Rectangular[/C][C]1.5733907812217[/C][C]2.75998858552682[/C][/ROW]
[ROW][C]Triangular[/C][C]1.55568523085138[/C][C]2.83229240081523[/C][/ROW]
[ROW][C]Biweight[/C][C]1.56453800603654[/C][C]2.80895275008944[/C][/ROW]
[ROW][C]Cosine[/C][C]1.56453800603654[/C][C]2.81793360268617[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.56453800603654[/C][C]2.79096083066781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279191&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279191&T=5

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
Gaussian1.560996895962482.87648924245068
Epanechnikov1.566308561073572.78428687538641
Rectangular1.57339078122172.75998858552682
Triangular1.555685230851382.83229240081523
Biweight1.564538006036542.80895275008944
Cosine1.564538006036542.81793360268617
Optcosine1.564538006036542.79096083066781


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')
}