FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 11 Dec 2017 15:40:13 +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/2017/Dec/11/t1513003246me48kqi6ejk9r6n.htm/, Retrieved Wed, 15 May 2024 13:17:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309005, Retrieved Wed, 15 May 2024 13:17:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

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] [Kernel Density Es...] [2017-12-11 14:40:13] [b96fd9fc55b2111e8fcab34a88822fe0] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.66
0.91
0.66
0.53
0.57
0.65
0.72
0.55
0.34
0.62
0.58
0.54
0.64
0.49
0.49
0.93
0.82
0.68
0.98
0.96
0.73
0.28
0.97
0.76
0.60
0.24
0.24
0.34
0.89
0.51
0.81
1.00
0.56
0.54
0.64
0.46
0.25
0.25
0.44
0.30
0.32
0.67
0.30
0.14
0.01
0.01
0.05
0.11
0.43
0.71
0.40
0.47
0.54
0.33
0.07
0.19
0.25
0.51
0.47
0.61
0.94
0.42
0.21
0.32

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309005&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309005&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center






Properties of Density Trace
Bandwidth0.101212465760185
#Observations64

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.101212465760185 \tabularnewline
#Observations & 64 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309005&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.101212465760185[/C][/ROW]
[ROW][C]#Observations[/C][C]64[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309005&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
Bandwidth0.101212465760185
#Observations64






Maximum Density Values
Kernelx-valuemax. density
Gaussian0.5534496268408951.44737977130535
Epanechnikov0.5409464973335671.40109620083821
Rectangular0.4940597616810881.43897995802588
Triangular0.5409464973335671.43305073780818
Biweight0.5471980620872311.41793169759662
Cosine0.5503238444640631.42286429663602
Optcosine0.5409464973335671.40751844467069

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.553449626840895 & 1.44737977130535 \tabularnewline
Epanechnikov & 0.540946497333567 & 1.40109620083821 \tabularnewline
Rectangular & 0.494059761681088 & 1.43897995802588 \tabularnewline
Triangular & 0.540946497333567 & 1.43305073780818 \tabularnewline
Biweight & 0.547198062087231 & 1.41793169759662 \tabularnewline
Cosine & 0.550323844464063 & 1.42286429663602 \tabularnewline
Optcosine & 0.540946497333567 & 1.40751844467069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309005&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]0.553449626840895[/C][C]1.44737977130535[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]0.540946497333567[/C][C]1.40109620083821[/C][/ROW]
[ROW][C]Rectangular[/C][C]0.494059761681088[/C][C]1.43897995802588[/C][/ROW]
[ROW][C]Triangular[/C][C]0.540946497333567[/C][C]1.43305073780818[/C][/ROW]
[ROW][C]Biweight[/C][C]0.547198062087231[/C][C]1.41793169759662[/C][/ROW]
[ROW][C]Cosine[/C][C]0.550323844464063[/C][C]1.42286429663602[/C][/ROW]
[ROW][C]Optcosine[/C][C]0.540946497333567[/C][C]1.40751844467069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309005&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
Gaussian0.5534496268408951.44737977130535
Epanechnikov0.5409464973335671.40109620083821
Rectangular0.4940597616810881.43897995802588
Triangular0.5409464973335671.43305073780818
Biweight0.5471980620872311.41793169759662
Cosine0.5503238444640631.42286429663602
Optcosine0.5409464973335671.40751844467069






Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown

\begin{tabular}{lllllllll}
\hline
Kernel Density Values \tabularnewline
x-value & Gaussian & Epanechnikov & Rectangular & Triangular & Biweight & Cosine & Optcosine \tabularnewline
Kernel Density Values are not shown \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309005&T=3

[TABLE]
[ROW][C]Kernel Density Values[/C][/ROW]
[ROW][C]x-value[/C][C]Gaussian[/C][C]Epanechnikov[/C][C]Rectangular[/C][C]Triangular[/C][C]Biweight[/C][C]Cosine[/C][C]Optcosine[/C][/ROW]
[ROW][C]Kernel Density Values are not shown[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309005&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309005&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:

Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown


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')
ab<-table.start()
ab<-table.row.start(ab)
ab<-table.element(ab,'Properties of Density Trace',2,TRUE)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'Bandwidth',header=TRUE)
ab<-table.element(ab,mydensity1$bw)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'#Observations',header=TRUE)
ab<-table.element(ab,mydensity1$n)
ab<-table.row.end(ab)
ab<-table.end(ab)
a <- ab
table.save(ab,file='mytable123.tab')
b<-table.start()
b<-table.row.start(b)
b<-table.element(b,'Maximum Density Values',3,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Kernel',1,TRUE)
b<-table.element(b,'x-value',1,TRUE)
b<-table.element(b,'max. density',1,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Gaussian',1,TRUE)
b<-table.element(b,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
b<-table.element(b,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Epanechnikov',1,TRUE)
b<-table.element(b,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
b<-table.element(b,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Rectangular',1,TRUE)
b<-table.element(b,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
b<-table.element(b,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Triangular',1,TRUE)
b<-table.element(b,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
b<-table.element(b,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Biweight',1,TRUE)
b<-table.element(b,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
b<-table.element(b,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Cosine',1,TRUE)
b<-table.element(b,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
b<-table.element(b,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Optcosine',1,TRUE)
b<-table.element(b,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
b<-table.element(b,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
b<-table.row.end(b)
b<-table.end(b)
a <- b[1]
table.save(b,file='mytable2a.tab')
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)
if (par2=='yes') {
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)
}
} else {
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values are not shown',8)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')