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 computationSat, 29 Dec 2012 10:25:00 -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/Dec/29/t1356794883htu4g03zbudnr6h.htm/, Retrieved Fri, 28 Nov 2025 20:07:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204884, Retrieved Fri, 28 Nov 2025 20:07:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact386

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] [prijs vliegtuigti...] [2012-09-21 20:50:58] [74be16979710d4c4e7c6647856088456]
- RMPD  [Histogram] [gemiddelde prijze...] [2012-12-29 14:54:13] [770959544eacfa1f4175753a9a1bfc9b]
- RMP       [Kernel Density Estimation] [gemiddelde prijze...] [2012-12-29 15:25:00] [d0e7cd87186a15776b36563906a5538f] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.86
86.79
82.52
86.87
81.62
82.66
89.87
92.04
79.74
77.75
79.12
76.37
75.01
77.6
77.81
81.7
76.47
74.72
84.43
86.72
70.99
75.43
74.14
73.3
71.97
69.27
74.13
76.4
72.26
72.1
87.82
91.62
82.69
85.76
86.87
93.09
83.73
84.49
87.37
89.13
83.2
83.77
93.68
93.09
88.59
87.88
87.89
89.38
89.13
89.58
90.22
91.44
91.04
92.1
97.54
99.12
100
99.68
100.08
99.9
99.63
99.45
99.63
99.46
96.91
97.65
102.1
103.57
104.59
104.79
101.31
104.8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204884&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204884&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Properties of Density Trace
Bandwidth3.72452907837217
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 3.72452907837217 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204884&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]3.72452907837217[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204884&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
Bandwidth3.72452907837217
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.54468157556960.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 87.6579441479184 & 0.0371903836919117 \tabularnewline
Epanechnikov & 87.0916312861744 & 0.0363500195280508 \tabularnewline
Rectangular & 87.5446815755696 & 0.0376767605985145 \tabularnewline
Triangular & 87.318156430872 & 0.0366348442262392 \tabularnewline
Biweight & 87.318156430872 & 0.0364102061614319 \tabularnewline
Cosine & 87.318156430872 & 0.0364766500732304 \tabularnewline
Optcosine & 87.2048938585232 & 0.0363531694897556 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204884&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]87.6579441479184[/C][C]0.0371903836919117[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.0916312861744[/C][C]0.0363500195280508[/C][/ROW]
[ROW][C]Rectangular[/C][C]87.5446815755696[/C][C]0.0376767605985145[/C][/ROW]
[ROW][C]Triangular[/C][C]87.318156430872[/C][C]0.0366348442262392[/C][/ROW]
[ROW][C]Biweight[/C][C]87.318156430872[/C][C]0.0364102061614319[/C][/ROW]
[ROW][C]Cosine[/C][C]87.318156430872[/C][C]0.0364766500732304[/C][/ROW]
[ROW][C]Optcosine[/C][C]87.2048938585232[/C][C]0.0363531694897556[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204884&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
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.54468157556960.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556






Maximum Density Values
Kernelx-valuemax. density
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.65794414791840.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 87.6579441479184 & 0.0371903836919117 \tabularnewline
Epanechnikov & 87.0916312861744 & 0.0363500195280508 \tabularnewline
Rectangular & 87.6579441479184 & 0.0376767605985145 \tabularnewline
Triangular & 87.318156430872 & 0.0366348442262392 \tabularnewline
Biweight & 87.318156430872 & 0.0364102061614319 \tabularnewline
Cosine & 87.318156430872 & 0.0364766500732304 \tabularnewline
Optcosine & 87.2048938585232 & 0.0363531694897556 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204884&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]87.6579441479184[/C][C]0.0371903836919117[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.0916312861744[/C][C]0.0363500195280508[/C][/ROW]
[ROW][C]Rectangular[/C][C]87.6579441479184[/C][C]0.0376767605985145[/C][/ROW]
[ROW][C]Triangular[/C][C]87.318156430872[/C][C]0.0366348442262392[/C][/ROW]
[ROW][C]Biweight[/C][C]87.318156430872[/C][C]0.0364102061614319[/C][/ROW]
[ROW][C]Cosine[/C][C]87.318156430872[/C][C]0.0364766500732304[/C][/ROW]
[ROW][C]Optcosine[/C][C]87.2048938585232[/C][C]0.0363531694897556[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204884&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204884&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
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.65794414791840.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556






Maximum Density Values
Kernelx-valuemax. density
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.77120672026710.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 87.6579441479184 & 0.0371903836919117 \tabularnewline
Epanechnikov & 87.0916312861744 & 0.0363500195280508 \tabularnewline
Rectangular & 87.7712067202671 & 0.0376767605985145 \tabularnewline
Triangular & 87.318156430872 & 0.0366348442262392 \tabularnewline
Biweight & 87.318156430872 & 0.0364102061614319 \tabularnewline
Cosine & 87.318156430872 & 0.0364766500732304 \tabularnewline
Optcosine & 87.2048938585232 & 0.0363531694897556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204884&T=4

[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]87.6579441479184[/C][C]0.0371903836919117[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]87.0916312861744[/C][C]0.0363500195280508[/C][/ROW]
[ROW][C]Rectangular[/C][C]87.7712067202671[/C][C]0.0376767605985145[/C][/ROW]
[ROW][C]Triangular[/C][C]87.318156430872[/C][C]0.0366348442262392[/C][/ROW]
[ROW][C]Biweight[/C][C]87.318156430872[/C][C]0.0364102061614319[/C][/ROW]
[ROW][C]Cosine[/C][C]87.318156430872[/C][C]0.0364766500732304[/C][/ROW]
[ROW][C]Optcosine[/C][C]87.2048938585232[/C][C]0.0363531694897556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204884&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204884&T=4

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
Gaussian87.65794414791840.0371903836919117
Epanechnikov87.09163128617440.0363500195280508
Rectangular87.77120672026710.0376767605985145
Triangular87.3181564308720.0366348442262392
Biweight87.3181564308720.0364102061614319
Cosine87.3181564308720.0364766500732304
Optcosine87.20489385852320.0363531694897556


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')
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')
}