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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, 26 Sep 2013 10:14:00 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Sep/26/t1380204893mlhsnbxaplu8yuc.htm/, Retrieved Mon, 29 Apr 2024 13:17:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=212127, Retrieved Mon, 29 Apr 2024 13:17:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [De goudkoers te B...] [2013-09-17 12:18:34] [53fdf1af79096e48ffa0efd17209e500]
- RM      [Kernel Density Estimation] [] [2013-09-26 14:14:00] [354a1e9bb909abf3036d55f04d250334] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271
43221
41373

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 7 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212127&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212127&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 time7 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Properties of Density Trace
Bandwidth3618.53613001985
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 3618.53613001985 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212127&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]3618.53613001985[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212127&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
Bandwidth3618.53613001985
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian19420.6905019134.45797941814943e-05
Epanechnikov20004.68913338214.29859718025708e-05
Rectangular21562.01881729984.43204293151596e-05
Triangular19518.02360715794.34970013900497e-05
Biweight19712.68981764764.33611145664402e-05
Cosine19615.35671240274.350707696136e-05
Optcosine19907.35602813734.307448734413e-05

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19420.690501913 & 4.45797941814943e-05 \tabularnewline
Epanechnikov & 20004.6891333821 & 4.29859718025708e-05 \tabularnewline
Rectangular & 21562.0188172998 & 4.43204293151596e-05 \tabularnewline
Triangular & 19518.0236071579 & 4.34970013900497e-05 \tabularnewline
Biweight & 19712.6898176476 & 4.33611145664402e-05 \tabularnewline
Cosine & 19615.3567124027 & 4.350707696136e-05 \tabularnewline
Optcosine & 19907.3560281373 & 4.307448734413e-05 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212127&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]19420.690501913[/C][C]4.45797941814943e-05[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20004.6891333821[/C][C]4.29859718025708e-05[/C][/ROW]
[ROW][C]Rectangular[/C][C]21562.0188172998[/C][C]4.43204293151596e-05[/C][/ROW]
[ROW][C]Triangular[/C][C]19518.0236071579[/C][C]4.34970013900497e-05[/C][/ROW]
[ROW][C]Biweight[/C][C]19712.6898176476[/C][C]4.33611145664402e-05[/C][/ROW]
[ROW][C]Cosine[/C][C]19615.3567124027[/C][C]4.350707696136e-05[/C][/ROW]
[ROW][C]Optcosine[/C][C]19907.3560281373[/C][C]4.307448734413e-05[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212127&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212127&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
Gaussian19420.6905019134.45797941814943e-05
Epanechnikov20004.68913338214.29859718025708e-05
Rectangular21562.01881729984.43204293151596e-05
Triangular19518.02360715794.34970013900497e-05
Biweight19712.68981764764.33611145664402e-05
Cosine19615.35671240274.350707696136e-05
Optcosine19907.35602813734.307448734413e-05






Maximum Density Values
Kernelx-valuemax. density
Gaussian19420.6905019134.45797941814943e-05
Epanechnikov20004.68913338214.29859718025708e-05
Rectangular21659.35192254464.43204293151596e-05
Triangular19518.02360715794.34970013900497e-05
Biweight19712.68981764764.33611145664402e-05
Cosine19615.35671240274.350707696136e-05
Optcosine19907.35602813734.307448734413e-05

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 19420.690501913 & 4.45797941814943e-05 \tabularnewline
Epanechnikov & 20004.6891333821 & 4.29859718025708e-05 \tabularnewline
Rectangular & 21659.3519225446 & 4.43204293151596e-05 \tabularnewline
Triangular & 19518.0236071579 & 4.34970013900497e-05 \tabularnewline
Biweight & 19712.6898176476 & 4.33611145664402e-05 \tabularnewline
Cosine & 19615.3567124027 & 4.350707696136e-05 \tabularnewline
Optcosine & 19907.3560281373 & 4.307448734413e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=212127&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]19420.690501913[/C][C]4.45797941814943e-05[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]20004.6891333821[/C][C]4.29859718025708e-05[/C][/ROW]
[ROW][C]Rectangular[/C][C]21659.3519225446[/C][C]4.43204293151596e-05[/C][/ROW]
[ROW][C]Triangular[/C][C]19518.0236071579[/C][C]4.34970013900497e-05[/C][/ROW]
[ROW][C]Biweight[/C][C]19712.6898176476[/C][C]4.33611145664402e-05[/C][/ROW]
[ROW][C]Cosine[/C][C]19615.3567124027[/C][C]4.350707696136e-05[/C][/ROW]
[ROW][C]Optcosine[/C][C]19907.3560281373[/C][C]4.307448734413e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=212127&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=212127&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
Gaussian19420.6905019134.45797941814943e-05
Epanechnikov20004.68913338214.29859718025708e-05
Rectangular21659.35192254464.43204293151596e-05
Triangular19518.02360715794.34970013900497e-05
Biweight19712.68981764764.33611145664402e-05
Cosine19615.35671240274.350707696136e-05
Optcosine19907.35602813734.307448734413e-05


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Goudkoers te Brussel (Euro) ; par2 = www.nbb.be ; par3 = De goudkoers te Brussel in Euro ; par4 = 12 ;
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')
}