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 computationTue, 02 Oct 2012 17:59:50 -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/02/t1349215213ya0l6olw7n5ai2f.htm/, Retrieved Sat, 04 May 2024 21:57:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=171572, Retrieved Sat, 04 May 2024 21:57:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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] [density ruwe aaro...] [2012-10-02 21:59:50] [4633288e60d40b4ed5f0b9573dd4d146] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83,4
83,5
89,5
85,8
77,4
67,5
63,7
59,4
62
62,4
58,1
58
56,3
61,4
59,8
54,3
47
50,5
48,1
58,8
70,4
71,9
73,3
83,5
90,1
101,3
98,3
106,7
109,9
111,1
119
120,7
104,5
121,6
129,6
124,5
130,1
142,3
140
143,3
113,4
113,8
120,7
112,9
115,5
121,9
119,3
111
114,2
113,5
94
83,2
82,8
85,8
88,7
105,3
113,1
113,8
109,4
113,9
118,1
125,2
121,5
109,2
120,8
134,3
144,4
132,9
112,3
114,5
122,4
126,4

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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=171572&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=171572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=171572&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'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth10.3805659119488
#Observations72

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 10.3805659119488 \tabularnewline
#Observations & 72 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=171572&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]10.3805659119488[/C][/ROW]
[ROW][C]#Observations[/C][C]72[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=171572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=171572&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
Bandwidth10.3805659119488
#Observations72






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.8557319137460.0160748203340675
Epanechnikov115.8557319137460.0149356068522208
Rectangular117.1056997843660.0142908339896981
Triangular113.9807801078160.0155278591412477
Biweight116.1682238814010.0152569893316802
Cosine116.1682238814010.0153846701591348
Optcosine116.1682238814010.0150292089248422

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.855731913746 & 0.0160748203340675 \tabularnewline
Epanechnikov & 115.855731913746 & 0.0149356068522208 \tabularnewline
Rectangular & 117.105699784366 & 0.0142908339896981 \tabularnewline
Triangular & 113.980780107816 & 0.0155278591412477 \tabularnewline
Biweight & 116.168223881401 & 0.0152569893316802 \tabularnewline
Cosine & 116.168223881401 & 0.0153846701591348 \tabularnewline
Optcosine & 116.168223881401 & 0.0150292089248422 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=171572&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]115.855731913746[/C][C]0.0160748203340675[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.855731913746[/C][C]0.0149356068522208[/C][/ROW]
[ROW][C]Rectangular[/C][C]117.105699784366[/C][C]0.0142908339896981[/C][/ROW]
[ROW][C]Triangular[/C][C]113.980780107816[/C][C]0.0155278591412477[/C][/ROW]
[ROW][C]Biweight[/C][C]116.168223881401[/C][C]0.0152569893316802[/C][/ROW]
[ROW][C]Cosine[/C][C]116.168223881401[/C][C]0.0153846701591348[/C][/ROW]
[ROW][C]Optcosine[/C][C]116.168223881401[/C][C]0.0150292089248422[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=171572&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=171572&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
Gaussian115.8557319137460.0160748203340675
Epanechnikov115.8557319137460.0149356068522208
Rectangular117.1056997843660.0142908339896981
Triangular113.9807801078160.0155278591412477
Biweight116.1682238814010.0152569893316802
Cosine116.1682238814010.0153846701591348
Optcosine116.1682238814010.0150292089248422






Maximum Density Values
Kernelx-valuemax. density
Gaussian115.8557319137460.0160748203340675
Epanechnikov115.8557319137460.0149356068522208
Rectangular117.4181917520210.0142908339896981
Triangular113.9807801078160.0155278591412477
Biweight116.1682238814010.0152569893316802
Cosine116.1682238814010.0153846701591348
Optcosine116.1682238814010.0150292089248422

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 115.855731913746 & 0.0160748203340675 \tabularnewline
Epanechnikov & 115.855731913746 & 0.0149356068522208 \tabularnewline
Rectangular & 117.418191752021 & 0.0142908339896981 \tabularnewline
Triangular & 113.980780107816 & 0.0155278591412477 \tabularnewline
Biweight & 116.168223881401 & 0.0152569893316802 \tabularnewline
Cosine & 116.168223881401 & 0.0153846701591348 \tabularnewline
Optcosine & 116.168223881401 & 0.0150292089248422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=171572&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]115.855731913746[/C][C]0.0160748203340675[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]115.855731913746[/C][C]0.0149356068522208[/C][/ROW]
[ROW][C]Rectangular[/C][C]117.418191752021[/C][C]0.0142908339896981[/C][/ROW]
[ROW][C]Triangular[/C][C]113.980780107816[/C][C]0.0155278591412477[/C][/ROW]
[ROW][C]Biweight[/C][C]116.168223881401[/C][C]0.0152569893316802[/C][/ROW]
[ROW][C]Cosine[/C][C]116.168223881401[/C][C]0.0153846701591348[/C][/ROW]
[ROW][C]Optcosine[/C][C]116.168223881401[/C][C]0.0150292089248422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=171572&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=171572&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
Gaussian115.8557319137460.0160748203340675
Epanechnikov115.8557319137460.0149356068522208
Rectangular117.4181917520210.0142908339896981
Triangular113.9807801078160.0155278591412477
Biweight116.1682238814010.0152569893316802
Cosine116.1682238814010.0153846701591348
Optcosine116.1682238814010.0150292089248422


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')
}