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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, 18 Dec 2014 00:11:30 +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/t1418861527wt2md5lt4eyen83.htm/, Retrieved Sun, 19 May 2024 19:19:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270741, Retrieved Sun, 19 May 2024 19:19:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95

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] [] [2014-12-18 00:11:30] [397b699eae6f3431a51b0bb18afa5c27] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2011
2203
2523
2565
2596
2545
1935
2386
2478
2457
2194
1736
1881
2520
2381
2419
2541
2514
1737
2221
2648
2159
2184
1745
1770
1871
2137
2283
2042
2099
1653
2254
2302
2233
1974
1684
1842
1592
2175
2366
2569
2894
2159
2877
2419
2305
1812
1514
1557
1606
1988
1901
1993
1993
1420
1927
2029
1899
1759
1496
2091
1850
2326
2212
2083
2048
1642
2014
1844
1846
1743
1337
1682
1512
2050
2108
1948
1927
1641
1916
1921
1858
1823
1367

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=270741&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=270741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270741&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
Bandwidth128.262726695482
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 128.262726695482 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270741&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]128.262726695482[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270741&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
Bandwidth128.262726695482
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian1944.762987267160.00108827678571499
Epanechnikov1981.186883316830.00107854464063253
Rectangular2022.163766372710.00109853394031419
Triangular1931.104026248530.00108200592723754
Biweight1958.421948285780.00107751400813837
Cosine1958.421948285780.00107898224386536
Optcosine1967.52792229820.00107751397137571

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1944.76298726716 & 0.00108827678571499 \tabularnewline
Epanechnikov & 1981.18688331683 & 0.00107854464063253 \tabularnewline
Rectangular & 2022.16376637271 & 0.00109853394031419 \tabularnewline
Triangular & 1931.10402624853 & 0.00108200592723754 \tabularnewline
Biweight & 1958.42194828578 & 0.00107751400813837 \tabularnewline
Cosine & 1958.42194828578 & 0.00107898224386536 \tabularnewline
Optcosine & 1967.5279222982 & 0.00107751397137571 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270741&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]1944.76298726716[/C][C]0.00108827678571499[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1981.18688331683[/C][C]0.00107854464063253[/C][/ROW]
[ROW][C]Rectangular[/C][C]2022.16376637271[/C][C]0.00109853394031419[/C][/ROW]
[ROW][C]Triangular[/C][C]1931.10402624853[/C][C]0.00108200592723754[/C][/ROW]
[ROW][C]Biweight[/C][C]1958.42194828578[/C][C]0.00107751400813837[/C][/ROW]
[ROW][C]Cosine[/C][C]1958.42194828578[/C][C]0.00107898224386536[/C][/ROW]
[ROW][C]Optcosine[/C][C]1967.5279222982[/C][C]0.00107751397137571[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270741&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270741&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
Gaussian1944.762987267160.00108827678571499
Epanechnikov1981.186883316830.00107854464063253
Rectangular2022.163766372710.00109853394031419
Triangular1931.104026248530.00108200592723754
Biweight1958.421948285780.00107751400813837
Cosine1958.421948285780.00107898224386536
Optcosine1967.52792229820.00107751397137571






Maximum Density Values
Kernelx-valuemax. density
Gaussian1944.762987267160.00108827678571499
Epanechnikov1981.186883316830.00107854464063253
Rectangular2026.716753378920.00109853394031419
Triangular1931.104026248530.00108200592723754
Biweight1958.421948285780.00107751400813837
Cosine1958.421948285780.00107898224386536
Optcosine1967.52792229820.00107751397137571

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 1944.76298726716 & 0.00108827678571499 \tabularnewline
Epanechnikov & 1981.18688331683 & 0.00107854464063253 \tabularnewline
Rectangular & 2026.71675337892 & 0.00109853394031419 \tabularnewline
Triangular & 1931.10402624853 & 0.00108200592723754 \tabularnewline
Biweight & 1958.42194828578 & 0.00107751400813837 \tabularnewline
Cosine & 1958.42194828578 & 0.00107898224386536 \tabularnewline
Optcosine & 1967.5279222982 & 0.00107751397137571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270741&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]1944.76298726716[/C][C]0.00108827678571499[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1981.18688331683[/C][C]0.00107854464063253[/C][/ROW]
[ROW][C]Rectangular[/C][C]2026.71675337892[/C][C]0.00109853394031419[/C][/ROW]
[ROW][C]Triangular[/C][C]1931.10402624853[/C][C]0.00108200592723754[/C][/ROW]
[ROW][C]Biweight[/C][C]1958.42194828578[/C][C]0.00107751400813837[/C][/ROW]
[ROW][C]Cosine[/C][C]1958.42194828578[/C][C]0.00107898224386536[/C][/ROW]
[ROW][C]Optcosine[/C][C]1967.5279222982[/C][C]0.00107751397137571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270741&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270741&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
Gaussian1944.762987267160.00108827678571499
Epanechnikov1981.186883316830.00107854464063253
Rectangular2026.716753378920.00109853394031419
Triangular1931.104026248530.00108200592723754
Biweight1958.421948285780.00107751400813837
Cosine1958.421948285780.00107898224386536
Optcosine1967.52792229820.00107751397137571


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')
}