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 computationWed, 19 Aug 2015 20:37:17 +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/Aug/19/t1440013079g5yr4immsky1l4t.htm/, Retrieved Thu, 16 May 2024 00:47:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280289, Retrieved Thu, 16 May 2024 00:47:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

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] [] [2015-08-19 19:37:17] [3e99441ea7f7f69c8fa4628f6be951c3] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12
20
20
14
25
15
20
21
15
28
11
22
22
27
24
23
24
21
20
19
25
16
24
21
22
25
23
20
21
22
25
23
19
27
21
19
25
16
24
24
18
28
15
17
18
26
18
22
19
17
26
21
26
21
12
20
20
24
24
22
21
20
23
19
24
21
16
17
23
20
19
18
18
21
20
17
20
25
15
17
17
24
21
22
18
22
20
21
21
20
18
25
23
21
20
21
20
22
15
24
22
21
17
23
22
23
16
18
25
18
14
20
19
18
22
21
14
5
25
21
11
20
9
15
23
21
9
24
16
20
15
18
22
21
21
21
20
24
15
24
18
24
24
15
19
20
26
26
18
23
13
16
19
22
21
11
23
18
19
15
8
15
21
25
14
21
18
18
12
24
17
20
24
22
15
22
26
17
23
19
21
23
19
18
16
23
13
18
23
21
23
16
17
20
18
20
19
26
9
23
9
13
27
22
12
18
6
17
22
22
23
19
20
17
18
24
20
18
23
27
25
24
12
16
16
24
23
24
24
26
19
28
23
21
19
23
23
20
18
20
28
21
25
18
24
28
9
22
26
28
18
23
22
15
24
12
12
20
25
24
23
18
20
22
20
25
28
25
14
16
24
13
19
18
16
8
27
23
20
20
26
23
24
21
15
22
25
23
16
26
25
23
24
26
20
24
14
28
25
21
19
22
22
21
17
21
23
16
15
24
25
23
19
24
14
20
23
12
22
18
21
23
22
28
20
22
24
19
9
23
23
22
20
23
24
17
19
17
23
19
24
15
22
25
27
23
16
24
22
27
28
23
25
21
22
25
25
19
24
21
18
17
17
26
8
25
22
20
22
17
24
20
19
26
13
20
26
21
24
23
16
24
18
21
17
19
22
23
27
22
22
25
26
22
25
23
8
24
14
17
21
21
25
18
20
25
20
24
22
16
20
21
22
15
21
25
16
28
22
19
17
23
28
19
24
16
19
19
12
16
15
17
23
21
20
19
20
20
23
22
20
24
21
23
22
21
26
16
28
24
28
14
16
22
18
23
18
22
13
20
24
24
25
23
24
22
24
24
24
25
27
27
14
21
17
23
25
20
21
24
27
12
26
22
24
24
20
22
23
22
21
13
21
20
18
19
25
24

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=280289&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=280289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280289&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
Bandwidth1.09395203318662
#Observations498

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1.09395203318662 \tabularnewline
#Observations & 498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280289&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1.09395203318662[/C][/ROW]
[ROW][C]#Observations[/C][C]498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280289&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
Bandwidth1.09395203318662
#Observations498






Maximum Density Values
Kernelx-valuemax. density
Gaussian22.48795344933250.0995491040962163
Epanechnikov22.02511646774160.10224411955697
Rectangular22.60366269473020.10703680173504
Triangular22.02511646774160.102762471517665
Biweight22.08297109044040.100416303174893
Cosine22.31438958123590.100214807281179
Optcosine22.02511646774160.101797529081266

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 22.4879534493325 & 0.0995491040962163 \tabularnewline
Epanechnikov & 22.0251164677416 & 0.10224411955697 \tabularnewline
Rectangular & 22.6036626947302 & 0.10703680173504 \tabularnewline
Triangular & 22.0251164677416 & 0.102762471517665 \tabularnewline
Biweight & 22.0829710904404 & 0.100416303174893 \tabularnewline
Cosine & 22.3143895812359 & 0.100214807281179 \tabularnewline
Optcosine & 22.0251164677416 & 0.101797529081266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280289&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]22.4879534493325[/C][C]0.0995491040962163[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]22.0251164677416[/C][C]0.10224411955697[/C][/ROW]
[ROW][C]Rectangular[/C][C]22.6036626947302[/C][C]0.10703680173504[/C][/ROW]
[ROW][C]Triangular[/C][C]22.0251164677416[/C][C]0.102762471517665[/C][/ROW]
[ROW][C]Biweight[/C][C]22.0829710904404[/C][C]0.100416303174893[/C][/ROW]
[ROW][C]Cosine[/C][C]22.3143895812359[/C][C]0.100214807281179[/C][/ROW]
[ROW][C]Optcosine[/C][C]22.0251164677416[/C][C]0.101797529081266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280289&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280289&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
Gaussian22.48795344933250.0995491040962163
Epanechnikov22.02511646774160.10224411955697
Rectangular22.60366269473020.10703680173504
Triangular22.02511646774160.102762471517665
Biweight22.08297109044040.100416303174893
Cosine22.31438958123590.100214807281179
Optcosine22.02511646774160.101797529081266


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')
}