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Author's title

Author

*Unverified author*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Sun, 07 Oct 2012 13:47:29 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/07/t1349632130us66ydtm1c6vig1.htm/, Retrieved Sat, 04 May 2024 17:13:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173066, Retrieved Sat, 04 May 2024 17:13:22 +0000

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User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [Treinkaartje enke...] [2012-09-23 12:19:17] [c97f1ed9e083b6e685d7991c70cc04e4]
- RMPD  [Histogram] [Treinticket 6 kla...] [2012-10-07 17:32:58] [c97f1ed9e083b6e685d7991c70cc04e4]
- RM        [Kernel Density Estimation] [Dichtheidsgrafiek...] [2012-10-07 17:47:29] [e9693728cfb785c84158f00c620f24e3] [Current]

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Dataseries X:

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Histogram

Boxplots

2.9
3
3
3
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3.5
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3.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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=173066&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=173066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173066&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Properties of Density Trace
Bandwidth	0.0590724511865354
#Observations	77

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.0590724511865354 \tabularnewline
#Observations & 77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173066&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.0590724511865354[/C][/ROW]
[ROW][C]#Observations[/C][C]77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173066&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth	0.0590724511865354
#Observations	77

Maximum Density Values
Kernel	x-value	max. density
Gaussian	3.29992613861229	3.16062228824446
Epanechnikov	3.29992613861229	2.65413040506155
Rectangular	3.20093388914591	2.73302348307334
Triangular	3.29992613861229	3.20512993476246
Biweight	3.29992613861229	2.80371356541951
Cosine	3.29992613861229	2.86035103428725
Optcosine	3.29992613861229	2.70487536985375

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 3.29992613861229 & 3.16062228824446 \tabularnewline
Epanechnikov & 3.29992613861229 & 2.65413040506155 \tabularnewline
Rectangular & 3.20093388914591 & 2.73302348307334 \tabularnewline
Triangular & 3.29992613861229 & 3.20512993476246 \tabularnewline
Biweight & 3.29992613861229 & 2.80371356541951 \tabularnewline
Cosine & 3.29992613861229 & 2.86035103428725 \tabularnewline
Optcosine & 3.29992613861229 & 2.70487536985375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173066&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]3.29992613861229[/C][C]3.16062228824446[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]3.29992613861229[/C][C]2.65413040506155[/C][/ROW]
[ROW][C]Rectangular[/C][C]3.20093388914591[/C][C]2.73302348307334[/C][/ROW]
[ROW][C]Triangular[/C][C]3.29992613861229[/C][C]3.20512993476246[/C][/ROW]
[ROW][C]Biweight[/C][C]3.29992613861229[/C][C]2.80371356541951[/C][/ROW]
[ROW][C]Cosine[/C][C]3.29992613861229[/C][C]2.86035103428725[/C][/ROW]
[ROW][C]Optcosine[/C][C]3.29992613861229[/C][C]2.70487536985375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173066&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernel	x-value	max. density
Gaussian	3.29992613861229	3.16062228824446
Epanechnikov	3.29992613861229	2.65413040506155
Rectangular	3.20093388914591	2.73302348307334
Triangular	3.29992613861229	3.20512993476246
Biweight	3.29992613861229	2.80371356541951
Cosine	3.29992613861229	2.86035103428725
Optcosine	3.29992613861229	2.70487536985375

Figure 1

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Postscript link

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Figure 2

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Figure 3

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PDF link

Figure 4

PNG link

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PDF link

Figure 5

PNG link

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PDF link

Figure 6

PNG link

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Figure 7

PNG link

Postscript link

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Parameters (Session):

par1 = 6 ; 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):

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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code