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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 computationTue, 13 Nov 2012 23:18:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/13/t1352866870mc1lvgjnl33xrft.htm/, Retrieved Sun, 28 Apr 2024 17:22:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=189225, Retrieved Sun, 28 Apr 2024 17:22:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

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] [problem3partb] [2012-11-14 04:18:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84.4
44.6
12.8
68.2
48.3
61.3
24.5
68
90.7
69.9
5.7
40.4
42.9
6.3
41.4
30.8
41.5
56.3
20
23.3
40.6
7.8
31.4
61.7
89.7
9.8
91.2
42.7
46.6
55.2
50.7
82.8
54.4
62.5
68.4
57.5
67.8
29.6
79.7
32.7
14.6
41.3
47.2
57.5
91.8
58.1
61.2
35.6
45.2
6.7
45.6
38.7
54.9
61.6
35.2
36.6
7.8
41.9
51.7
11.7
28.5
54.5
46.9
38.5
50.7
12.1
10.4
59.2
7.1
49.1
53.1
30.6
41.6
57.1
65.5
33.7
38.1
55.2
28.1
34.7
56.8
48.5
46.6
47.7
16.8
46.5
39.9
47.5
8.9
58.2
54.6
58.4
51.9
9
39.1
28.4
8.1
49.5
33.7
72.8
55.5
59.6
31
81.6
90.7
43.7
67.3
41
53.7
38.8
47.3
41.1
52.5
29.7
62.3
43.7
37.7
46.1
53.6
34.9
43.7
39.7
48.4
11.7
40.9
34.9
37.8
35
37
55.2
36.3
45.7
65.1
55.2
39.7
6
53.2
32
47.7
71.8
39.1
42.5
40
41.9
58.2
21.4
31.7
58.1
44.3
47.3
33
64.8
10.8
40.6
70
45
35.8
35.4
50.2
49.7
9.5
37.7
73.8
75.9
66.5
52
57.3
37.2
30.5
47.3
57.1
34.8
57.6
52.4
45.8
54.7
28.1
50.4
28.6
42.3
48.7
43.1
52.9
67.5
31.7
57.3
61.1
70.1
45.3
40.5
41.9
36.3
34.4
35.6
43.2
11.9
34.5
48.5
55.6
70.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189225&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]5 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=189225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189225&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Properties of Density Trace
Bandwidth5.93439
#Observations200

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 5.93439 \tabularnewline
#Observations & 200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189225&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]5.93439[/C][/ROW]
[ROW][C]#Observations[/C][C]200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189225&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
Bandwidth5.93439
#Observations200






Maximum Density Values
Kernelx-valuemax. density
Gaussian42.91476452054790.0239828335867519
Epanechnikov45.77283904109590.0238597497279216
Rectangular45.05832041095890.0248848549077349
Triangular44.58197465753420.0238532794354504
Biweight44.10562890410960.0238630866759632
Cosine43.62928315068490.0238903507757731
Optcosine45.29649328767120.0238392028027066

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 42.9147645205479 & 0.0239828335867519 \tabularnewline
Epanechnikov & 45.7728390410959 & 0.0238597497279216 \tabularnewline
Rectangular & 45.0583204109589 & 0.0248848549077349 \tabularnewline
Triangular & 44.5819746575342 & 0.0238532794354504 \tabularnewline
Biweight & 44.1056289041096 & 0.0238630866759632 \tabularnewline
Cosine & 43.6292831506849 & 0.0238903507757731 \tabularnewline
Optcosine & 45.2964932876712 & 0.0238392028027066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189225&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]42.9147645205479[/C][C]0.0239828335867519[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]45.7728390410959[/C][C]0.0238597497279216[/C][/ROW]
[ROW][C]Rectangular[/C][C]45.0583204109589[/C][C]0.0248848549077349[/C][/ROW]
[ROW][C]Triangular[/C][C]44.5819746575342[/C][C]0.0238532794354504[/C][/ROW]
[ROW][C]Biweight[/C][C]44.1056289041096[/C][C]0.0238630866759632[/C][/ROW]
[ROW][C]Cosine[/C][C]43.6292831506849[/C][C]0.0238903507757731[/C][/ROW]
[ROW][C]Optcosine[/C][C]45.2964932876712[/C][C]0.0238392028027066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189225&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
Gaussian42.91476452054790.0239828335867519
Epanechnikov45.77283904109590.0238597497279216
Rectangular45.05832041095890.0248848549077349
Triangular44.58197465753420.0238532794354504
Biweight44.10562890410960.0238630866759632
Cosine43.62928315068490.0238903507757731
Optcosine45.29649328767120.0238392028027066


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 5.93439 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 5.93439 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
par3 <- '512'
par2 <- 'no'
par1 <- '0'
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')
}