FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationFri, 03 Oct 2014 18:35:18 +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/2014/Oct/03/t1412357836u6q3r8rw0qudk3f.htm/, Retrieved Fri, 10 May 2024 13:50:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=238484, Retrieved Fri, 10 May 2024 13:50:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [] [2014-10-03 17:35:18] [bc3b0a9d08b571f2c6b79bb1a1231eac] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
250.8
247.6
237.8
226.4
217.2
211.4
207.6
204.3
197.5
193.6
192.3
192
196.1
191.9
185.6
179.4
173.9
169.2
166.8
165.2
161.4
160.8
163.7
170.8
182.7
190.9
197.8
205.1
210.7
220.2
229.7
237.1
241.6
250.4
258.6
269.9
283.2
289.6
281.8
274.7
267.6
261.4
260.5
260.7
254.2
250.5
253.4
263.7
276.2
273.8
265.9
258.4
253.5
250.7
252.8
255.3
251.2
252.5
257.8
269.9
291.6
298.9
295.6
292.1
290.9
290.6
298
304
304.3
309.8
322.3
340.2
369.3
376.7
379.7
379.5
377.8
381.6
394.6
399.3
400.4
408.2
419.1
437.7

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=238484&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=238484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Bandwidth23.4650541484801
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 23.4650541484801 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=238484&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]23.4650541484801[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=238484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Bandwidth23.4650541484801
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular230.1798777822320.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 260.423599936758 & 0.00667189925562377 \tabularnewline
Epanechnikov & 264.510589417099 & 0.00634791778764594 \tabularnewline
Rectangular & 230.179877782232 & 0.00629762774496538 \tabularnewline
Triangular & 257.971406248553 & 0.00658752485504027 \tabularnewline
Biweight & 262.058395728894 & 0.00643528667394736 \tabularnewline
Cosine & 262.058395728894 & 0.00646951851332735 \tabularnewline
Optcosine & 262.875793624963 & 0.00637470798844488 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=238484&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]260.423599936758[/C][C]0.00667189925562377[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]264.510589417099[/C][C]0.00634791778764594[/C][/ROW]
[ROW][C]Rectangular[/C][C]230.179877782232[/C][C]0.00629762774496538[/C][/ROW]
[ROW][C]Triangular[/C][C]257.971406248553[/C][C]0.00658752485504027[/C][/ROW]
[ROW][C]Biweight[/C][C]262.058395728894[/C][C]0.00643528667394736[/C][/ROW]
[ROW][C]Cosine[/C][C]262.058395728894[/C][C]0.00646951851332735[/C][/ROW]
[ROW][C]Optcosine[/C][C]262.875793624963[/C][C]0.00637470798844488[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=238484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular230.1798777822320.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488






Maximum Density Values
Kernelx-valuemax. density
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular230.99727567830.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 260.423599936758 & 0.00667189925562377 \tabularnewline
Epanechnikov & 264.510589417099 & 0.00634791778764594 \tabularnewline
Rectangular & 230.9972756783 & 0.00629762774496538 \tabularnewline
Triangular & 257.971406248553 & 0.00658752485504027 \tabularnewline
Biweight & 262.058395728894 & 0.00643528667394736 \tabularnewline
Cosine & 262.058395728894 & 0.00646951851332735 \tabularnewline
Optcosine & 262.875793624963 & 0.00637470798844488 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=238484&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]260.423599936758[/C][C]0.00667189925562377[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]264.510589417099[/C][C]0.00634791778764594[/C][/ROW]
[ROW][C]Rectangular[/C][C]230.9972756783[/C][C]0.00629762774496538[/C][/ROW]
[ROW][C]Triangular[/C][C]257.971406248553[/C][C]0.00658752485504027[/C][/ROW]
[ROW][C]Biweight[/C][C]262.058395728894[/C][C]0.00643528667394736[/C][/ROW]
[ROW][C]Cosine[/C][C]262.058395728894[/C][C]0.00646951851332735[/C][/ROW]
[ROW][C]Optcosine[/C][C]262.875793624963[/C][C]0.00637470798844488[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=238484&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular230.99727567830.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488






Maximum Density Values
Kernelx-valuemax. density
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular264.5105894170990.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 260.423599936758 & 0.00667189925562377 \tabularnewline
Epanechnikov & 264.510589417099 & 0.00634791778764594 \tabularnewline
Rectangular & 264.510589417099 & 0.00629762774496538 \tabularnewline
Triangular & 257.971406248553 & 0.00658752485504027 \tabularnewline
Biweight & 262.058395728894 & 0.00643528667394736 \tabularnewline
Cosine & 262.058395728894 & 0.00646951851332735 \tabularnewline
Optcosine & 262.875793624963 & 0.00637470798844488 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=238484&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]260.423599936758[/C][C]0.00667189925562377[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]264.510589417099[/C][C]0.00634791778764594[/C][/ROW]
[ROW][C]Rectangular[/C][C]264.510589417099[/C][C]0.00629762774496538[/C][/ROW]
[ROW][C]Triangular[/C][C]257.971406248553[/C][C]0.00658752485504027[/C][/ROW]
[ROW][C]Biweight[/C][C]262.058395728894[/C][C]0.00643528667394736[/C][/ROW]
[ROW][C]Cosine[/C][C]262.058395728894[/C][C]0.00646951851332735[/C][/ROW]
[ROW][C]Optcosine[/C][C]262.875793624963[/C][C]0.00637470798844488[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=238484&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular264.5105894170990.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488






Maximum Density Values
Kernelx-valuemax. density
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular265.3279873131670.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 260.423599936758 & 0.00667189925562377 \tabularnewline
Epanechnikov & 264.510589417099 & 0.00634791778764594 \tabularnewline
Rectangular & 265.327987313167 & 0.00629762774496538 \tabularnewline
Triangular & 257.971406248553 & 0.00658752485504027 \tabularnewline
Biweight & 262.058395728894 & 0.00643528667394736 \tabularnewline
Cosine & 262.058395728894 & 0.00646951851332735 \tabularnewline
Optcosine & 262.875793624963 & 0.00637470798844488 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=238484&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]260.423599936758[/C][C]0.00667189925562377[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]264.510589417099[/C][C]0.00634791778764594[/C][/ROW]
[ROW][C]Rectangular[/C][C]265.327987313167[/C][C]0.00629762774496538[/C][/ROW]
[ROW][C]Triangular[/C][C]257.971406248553[/C][C]0.00658752485504027[/C][/ROW]
[ROW][C]Biweight[/C][C]262.058395728894[/C][C]0.00643528667394736[/C][/ROW]
[ROW][C]Cosine[/C][C]262.058395728894[/C][C]0.00646951851332735[/C][/ROW]
[ROW][C]Optcosine[/C][C]262.875793624963[/C][C]0.00637470798844488[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=238484&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=238484&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
Gaussian260.4235999367580.00667189925562377
Epanechnikov264.5105894170990.00634791778764594
Rectangular265.3279873131670.00629762774496538
Triangular257.9714062485530.00658752485504027
Biweight262.0583957288940.00643528667394736
Cosine262.0583957288940.00646951851332735
Optcosine262.8757936249630.00637470798844488


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')
}