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 computationTue, 09 Apr 2019 22:23:13 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2019/Apr/09/t1554841539fe1vkmsq76fx9i7.htm/, Retrieved Sat, 04 May 2024 18:40:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=318773, Retrieved Sat, 04 May 2024 18:40:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94

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] [] [2019-04-09 20:23:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.4
19.2
23.6
21
10.9
18.4
16.5
14.5
14.8
23.8
31.5
11.7
22.3
21.9
8.7
11.4
27.3
37.4
9.1
10
14.8
2.8
33
4.3
20
19.4
35.4
15.9
31.2
14.5
8.5
18.5
3
12.9
2.2
17.9
6
36.6
5.6
8.4
15.7
10.3
13.4
24.6
20.3
9.6
13
18.6
26.2
17.8
20.6
8.7
4.3
9.7
6.6
5.3
23.7
18.1
3.3
16.4
3
10
9.5
16.1
25.1
10.3
21.6
3.6
6.8
15.7
17
19.3
7.9
5.8
9.8
3.6
15.7
3.8
9.2
1.6
3.4
15.1
26.6
20.8
31
33.5
20.1
10.4
11.4
31.4
13.3
6.1
33.2
6
14.7
12.3
24.3
22.5
32.3
31.4
17
14.7
14.2
12.1
13.9
10.9
4.4
23.5
9.5
10.7
29.8
6.6
16.7
7.7
21
4.3
13.4
7.8
10.2
20.3
28.5
13.6
36.8
6.8
16.9
21.9
30.3
2.4
22.1
35.2
20.7
15.8
16.8
8.4
21.1
32.9
56.3
22.3
12
15.5
5
7
30.5
29
31
10.7
5.4
25.3
27.4
8
30.6
6.7
13.9
18.7
32.3
13
3.2
19.4
11.2
10.3
17.7
14.2
12.6
32.7
12.9
26.6
13
16.5
11.6
18.3
22.8
6.6
3.6
15.9
19.7
6
2.7
22.4
7.8
14.4
1
22.2
27.9
28.5
8.5
3.7
19.3
4.3
9.6
50.7
10.2
11.5
26.1
14.8
18.9
15.6
7.3
35.4
41.5
20.6
14.7
20
27
6.9
13.7
18.6
23.1
18.4
4.3
1.3
12.6
25.2
23.3
3.4
18.4
5.4
31.3
5.7
12.7
24.5
10.5
20.4
28.4
17.6
12.9
27.8
12.7
34.1
11.2
11.7
13.4
21.8
1
12.6
27.5
17.9
20
27.3
28.1
16.2
6.1
30.4
31.5
13.1
24.3
13.7
9.8
3.3
16
4.3
18.8
18.3
0.8
0.4
13.2
10.1
19.6
22.8
20.1
33.8
58.2
2.9
27.1
8.4
35.4
16.4
12.8
20
16.7
28.7
21.1
4.7
10.3
35
8.2
24.6
36.3
6.1
7.7
19.9
9.7
5.7
26.8
18.2
20.1
20.2
3.6
16.1
17.8
7.2
11.1
18.1
11.5
24.7
14.8
8.7
19.2
31.2
5.9
11.5
21.1
17.7
12.9
29.2
14.6
15.7
24
6.9
11
36.6
20.4
28.5
15.5
22.9
10
27.7
14.5
16.4
16.1
40.2
3.8
23
3.3
34.7
47.8
8.4
17.9
24
9.3
8.2
2.3
22.5
32.4
18.8
4.1
4
8.4
20.4
33.6
16.2
7.9
6.5
38.9
16.3
5.9
15.2
23.4
28.2
35.2
5.8
7.9
4.7
8.6
11.9
15
16.6
21.5
25.8
23
5.5
15.6
19.4
16.9
8.1
1.5
24
18
36.3
29.9
24
8.4
26.3
17.7
24.1
8.9
13.9
31.1
21.3
5.6
22.6
34.5
29.8
1.7
25.9
4.5
37
19.2
25
13.8
19.1
17.3
5.4
24
34.3
21
30.9
2.7
3.7
3.7
8.9
22.3
26.2
27.4
30.7
44.7
9.5
12
10.7
8.6
23.2
10.5
1.5
26.1
27.3
22.7
32.9
10.5
12.8
20.2
11.3
39.7
5.8
12.3
24.5
8.3
35.2
30.9
17.6
33.3
12.2
43.8
33.5
10.3
14.6
13.9
7
27
8.9
18.8
7.9
11
32.6
12.1
5.7
15.9
11.7
33.2
7.4
12.4
21.8
2
13.3
26.8
10.5
24
13.3
30.3
16.3
21.5
6.5
1
7.5
15.2
35.5
12
27.5
2.8
19.2
20.2
22.9
5.5
6.9
7.3
11
37
28.5
21
15.3
13.5
10.1
24.5
21
12.8
39.5
14.9
22.5
14.4
11.6
21.7
13.5
21
5.7
6.9
8.8
13.1
8.6
9.9
17
42.9
20.9
7.9
3
16.2
2.2
12.3
0.5
14.1
19.2
6.5
23.9
23.5
21.6
30.1
11.4
12.8
11.6
7.1
14.2
25.7
21.1
4.9
15.6
20.5
34
11.3
50.8
14.5
14.4
20.5
27.2
10.5
24.5
25
15.1
6.4
17
8.4
30
20.8
2.5
32.8
25.2
7
4.7
6
14
4.2
19.2
27
5.6
15.5
11.5
56.4
1.4
9
5.9
12
19.4
27.2
12.2
8.3
39.8
24.7
23.8
20.3
15.6
27.7
8.1
13.6
40.7
3
38.2
13.5
21.4
25.9
32.9
12.5
20.7
18.6
22.4
23.8
9.4
11.6
16.8
11
10.2
10.8
11.3
8.3
30
18.9
5.7
18.3
14.2
13.1
2.9
2.8
14.4
13.1
11.4
33.3
16.1
6.8
15.5
26.1
23.2
22.5
12
4.2
25.3
24.7
1
18.2
47
9.1
45.5
3.3
21.2
6.2
9.4
2.3
10.2
4.9
22.7
9.3
3.2
21.4
1.1
12
6.9
25.9
39.8
3.3
23.7
23.5
14.3
8.7
11.7
20.9
7.4
3.3
13.2
27.1
14.6
17.4
5.5
45.8
4
12.3
4.3
18.7
14.8
9.9
18.3
23.3
9.3
8.3
7
44.5
33.9
2.7
4.7
13.4
22.4
14.1
18.6
15.8
20.6
19.3
9.7
7.4
11.9
29
14.8
20.9
23
27.5
15.9
9.3
21.6
10.3
6.5
9.5
27.6
20.7
1.2
13.9
7.6
10.8
23.7
38.6
31.3
30.2
8.6
7.6
25.6
5.2
17.9
14.3
29.9
13.5
5.1
8.7
23.8
6.9
20.2
2.1
8.2
23.8
22.1
11.2
15.4
16.9
19.8
5.5
20.2
17.2
11.4
8.1
4.2
25.2
14.1
32.3
9.6
5.8
13.1
44.3
24.7
16.7
29.6
32.6
16.7
15.8
16.8
18.3
11.6
11
3.1
7.7
5.1
18.4
22.2
14.2
19.1
17
18.8
10.6
5.1
2.2
24.1
35.2
16.3
3.8
30.8
7.5
36.9
6.1
14.6
43.9
11.7
20.4
17.8
31.4
12.7
12.8
38.3
15
17.7
26.4
20.1
32.1
4.4
20.9
6.7

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318773&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=318773&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318773&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Properties of Density Trace
Bandwidth2.43754909747795
#Observations774

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 2.43754909747795 \tabularnewline
#Observations & 774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318773&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]2.43754909747795[/C][/ROW]
[ROW][C]#Observations[/C][C]774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318773&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318773&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
Bandwidth2.43754909747795
#Observations774






Maximum Density Values
Kernelx-valuemax. density
Gaussian11.93777184609340.0385791833062144
Epanechnikov11.79603937136760.0386229013999169
Rectangular10.66217957356140.0390554635083949
Triangular11.37084194719030.0386167155274497
Biweight11.51257442191610.0385394800476805
Cosine11.65430689664180.0385355513838872
Optcosine11.79603937136760.03858672469079

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 11.9377718460934 & 0.0385791833062144 \tabularnewline
Epanechnikov & 11.7960393713676 & 0.0386229013999169 \tabularnewline
Rectangular & 10.6621795735614 & 0.0390554635083949 \tabularnewline
Triangular & 11.3708419471903 & 0.0386167155274497 \tabularnewline
Biweight & 11.5125744219161 & 0.0385394800476805 \tabularnewline
Cosine & 11.6543068966418 & 0.0385355513838872 \tabularnewline
Optcosine & 11.7960393713676 & 0.03858672469079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=318773&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]11.9377718460934[/C][C]0.0385791833062144[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]11.7960393713676[/C][C]0.0386229013999169[/C][/ROW]
[ROW][C]Rectangular[/C][C]10.6621795735614[/C][C]0.0390554635083949[/C][/ROW]
[ROW][C]Triangular[/C][C]11.3708419471903[/C][C]0.0386167155274497[/C][/ROW]
[ROW][C]Biweight[/C][C]11.5125744219161[/C][C]0.0385394800476805[/C][/ROW]
[ROW][C]Cosine[/C][C]11.6543068966418[/C][C]0.0385355513838872[/C][/ROW]
[ROW][C]Optcosine[/C][C]11.7960393713676[/C][C]0.03858672469079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=318773&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318773&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
Gaussian11.93777184609340.0385791833062144
Epanechnikov11.79603937136760.0386229013999169
Rectangular10.66217957356140.0390554635083949
Triangular11.37084194719030.0386167155274497
Biweight11.51257442191610.0385394800476805
Cosine11.65430689664180.0385355513838872
Optcosine11.79603937136760.03858672469079






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=318773&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=318773&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=318773&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):
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')
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')