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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, 11 Oct 2012 12:57:20 -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/2012/Oct/11/t13499746984gkfolncbheelaz.htm/, Retrieved Sat, 27 Apr 2024 20:23:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175170, Retrieved Sat, 27 Apr 2024 20:23:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152

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] [Ontvangsten geïnd...] [2012-10-07 17:57:08] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP   [Central Tendency] [Centrummaten ontv...] [2012-10-11 15:49:27] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RM D    [Mean versus Median] [Gemiddelde versus...] [2012-10-11 16:06:05] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RMP       [Histogram] [inkomsten schatki...] [2012-10-11 16:42:04] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- R P         [Histogram] [frequentietabel s...] [2012-10-11 16:48:19] [7e0b1fc7e94581fb4f84255f8aa2fbc5]
- RM              [Kernel Density Estimation] [Dichtheidsgrafiek...] [2012-10-11 16:57:20] [1fc6f30e88849aa85fd62e34f240f44c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6848
5772
5251
11232
5908
6812
9962
6155
5673
7985
5780
11999
6973
5817
5844
11178
5533
6870
9521
5363
6031
9245
5621
11802
8364
6286
5071
10773
5821
7794
10636
6405
5811
8981
6228
11950
7523
6067
4825
12162
6989
8012
10893
6647
5938
9005
6262
12022
7683
6004
4724
10343
6604
7241
9331
6418
7094
10340
6814
12003
7481
5452
6380
11425
5905
8536
10785
6672
7293
9809
5658
12364
8078
5269
7787
11729
6236
8576
11216
6814
6019
9351
5464
12518

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175170&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175170&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'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth848.188620411631
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 848.188620411631 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175170&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]848.188620411631[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175170&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
Bandwidth848.188620411631
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian6213.291429557990.00021255960988803
Epanechnikov6364.561077962730.000204580284903601
Rectangular6641.888766704740.000206636875084383
Triangular6213.291429557990.000207401831714836
Biweight6288.926253760360.000206421354802049
Cosine6288.926253760360.000207242895278406
Optcosine6339.349469895270.000205087599759046

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 6213.29142955799 & 0.00021255960988803 \tabularnewline
Epanechnikov & 6364.56107796273 & 0.000204580284903601 \tabularnewline
Rectangular & 6641.88876670474 & 0.000206636875084383 \tabularnewline
Triangular & 6213.29142955799 & 0.000207401831714836 \tabularnewline
Biweight & 6288.92625376036 & 0.000206421354802049 \tabularnewline
Cosine & 6288.92625376036 & 0.000207242895278406 \tabularnewline
Optcosine & 6339.34946989527 & 0.000205087599759046 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175170&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]6213.29142955799[/C][C]0.00021255960988803[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]6364.56107796273[/C][C]0.000204580284903601[/C][/ROW]
[ROW][C]Rectangular[/C][C]6641.88876670474[/C][C]0.000206636875084383[/C][/ROW]
[ROW][C]Triangular[/C][C]6213.29142955799[/C][C]0.000207401831714836[/C][/ROW]
[ROW][C]Biweight[/C][C]6288.92625376036[/C][C]0.000206421354802049[/C][/ROW]
[ROW][C]Cosine[/C][C]6288.92625376036[/C][C]0.000207242895278406[/C][/ROW]
[ROW][C]Optcosine[/C][C]6339.34946989527[/C][C]0.000205087599759046[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175170&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
Gaussian6213.291429557990.00021255960988803
Epanechnikov6364.561077962730.000204580284903601
Rectangular6641.888766704740.000206636875084383
Triangular6213.291429557990.000207401831714836
Biweight6288.926253760360.000206421354802049
Cosine6288.926253760360.000207242895278406
Optcosine6339.349469895270.000205087599759046






Maximum Density Values
Kernelx-valuemax. density
Gaussian6213.291429557990.00021255960988803
Epanechnikov6364.561077962730.000204580284903601
Rectangular6667.10037477220.000206636875084383
Triangular6213.291429557990.000207401831714836
Biweight6288.926253760360.000206421354802049
Cosine6288.926253760360.000207242895278406
Optcosine6339.349469895270.000205087599759046

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 6213.29142955799 & 0.00021255960988803 \tabularnewline
Epanechnikov & 6364.56107796273 & 0.000204580284903601 \tabularnewline
Rectangular & 6667.1003747722 & 0.000206636875084383 \tabularnewline
Triangular & 6213.29142955799 & 0.000207401831714836 \tabularnewline
Biweight & 6288.92625376036 & 0.000206421354802049 \tabularnewline
Cosine & 6288.92625376036 & 0.000207242895278406 \tabularnewline
Optcosine & 6339.34946989527 & 0.000205087599759046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175170&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]6213.29142955799[/C][C]0.00021255960988803[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]6364.56107796273[/C][C]0.000204580284903601[/C][/ROW]
[ROW][C]Rectangular[/C][C]6667.1003747722[/C][C]0.000206636875084383[/C][/ROW]
[ROW][C]Triangular[/C][C]6213.29142955799[/C][C]0.000207401831714836[/C][/ROW]
[ROW][C]Biweight[/C][C]6288.92625376036[/C][C]0.000206421354802049[/C][/ROW]
[ROW][C]Cosine[/C][C]6288.92625376036[/C][C]0.000207242895278406[/C][/ROW]
[ROW][C]Optcosine[/C][C]6339.34946989527[/C][C]0.000205087599759046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175170&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175170&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
Gaussian6213.291429557990.00021255960988803
Epanechnikov6364.561077962730.000204580284903601
Rectangular6667.10037477220.000206636875084383
Triangular6213.291429557990.000207401831714836
Biweight6288.926253760360.000206421354802049
Cosine6288.926253760360.000207242895278406
Optcosine6339.349469895270.000205087599759046


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 0 ; 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')
}