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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 computationMon, 14 Aug 2017 21:21:18 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/14/t1502738586j19jv92zyag1b4z.htm/, Retrieved Mon, 13 May 2024 19:03:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307252, Retrieved Mon, 13 May 2024 19:03:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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] [] [2017-08-14 19:21:18] [b5765487180b26865894987d1ded8bd3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
64 800
62 400
66 000
52 800
68 400
67 200
72 000
74 400
82 800
72 000
68 400
85 200
72 000
54 000
63 600
48 000
67 200
55 200
73 200
66 000
69 600
78 000
76 800
91 200
66 000
55 200
61 200
44 400
63 600
49 200
69 600
66 000
58 800
84 000
75 600
86 400
64 800
60 000
54 000
44 400
58 800
52 800
72 000
69 600
60 000
80 400
74 400
96 000
76 800
46 800
46 800
46 800
55 200
55 200
74 400
68 400
61 200
76 800
70 800
102 000
80 400
46 800
49 200
40 800
56 400
64 800
81 600
80 400
64 800
75 600
67 200
96 000
73 200
58 800
52 800
39 600
58 800
70 800
82 800
78 000
57 600
82 800
64 800
99 600
82 800
60 000
55 200
37 200
58 800
56 400
85 200
85 200
64 800
84 000
62 400
97 200
82 800
61 200
46 800
32 400
63 600
61 200
80 400
92 400
68 400
76 800
57 600
99 600

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307252&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307252&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307252&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Properties of Density Trace
Bandwidth5055.38445503143
#Observations108

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 5055.38445503143 \tabularnewline
#Observations & 108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307252&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]5055.38445503143[/C][/ROW]
[ROW][C]#Observations[/C][C]108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307252&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307252&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
Bandwidth5055.38445503143
#Observations108






Maximum Density Values
Kernelx-valuemax. density
Gaussian64559.90970477982.65049531073635e-05
Epanechnikov63582.09848432782.64032617511891e-05
Rectangular63582.09848432782.73342755559791e-05
Triangular64755.47194887012.66234674963253e-05
Biweight64168.7852165992.64029420922208e-05
Cosine64364.34746068942.64211935579809e-05
Optcosine63582.09848432782.6416231872311e-05

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 64559.9097047798 & 2.65049531073635e-05 \tabularnewline
Epanechnikov & 63582.0984843278 & 2.64032617511891e-05 \tabularnewline
Rectangular & 63582.0984843278 & 2.73342755559791e-05 \tabularnewline
Triangular & 64755.4719488701 & 2.66234674963253e-05 \tabularnewline
Biweight & 64168.785216599 & 2.64029420922208e-05 \tabularnewline
Cosine & 64364.3474606894 & 2.64211935579809e-05 \tabularnewline
Optcosine & 63582.0984843278 & 2.6416231872311e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307252&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]64559.9097047798[/C][C]2.65049531073635e-05[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]63582.0984843278[/C][C]2.64032617511891e-05[/C][/ROW]
[ROW][C]Rectangular[/C][C]63582.0984843278[/C][C]2.73342755559791e-05[/C][/ROW]
[ROW][C]Triangular[/C][C]64755.4719488701[/C][C]2.66234674963253e-05[/C][/ROW]
[ROW][C]Biweight[/C][C]64168.785216599[/C][C]2.64029420922208e-05[/C][/ROW]
[ROW][C]Cosine[/C][C]64364.3474606894[/C][C]2.64211935579809e-05[/C][/ROW]
[ROW][C]Optcosine[/C][C]63582.0984843278[/C][C]2.6416231872311e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307252&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307252&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
Gaussian64559.90970477982.65049531073635e-05
Epanechnikov63582.09848432782.64032617511891e-05
Rectangular63582.09848432782.73342755559791e-05
Triangular64755.47194887012.66234674963253e-05
Biweight64168.7852165992.64029420922208e-05
Cosine64364.34746068942.64211935579809e-05
Optcosine63582.09848432782.6416231872311e-05






Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown

\begin{tabular}{lllllllll}
\hline
Kernel Density Values \tabularnewline
x-value & Gaussian & Epanechnikov & Rectangular & Triangular & Biweight & Cosine & Optcosine \tabularnewline
Kernel Density Values are not shown \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307252&T=3

[TABLE]
[ROW][C]Kernel Density Values[/C][/ROW]
[ROW][C]x-value[/C][C]Gaussian[/C][C]Epanechnikov[/C][C]Rectangular[/C][C]Triangular[/C][C]Biweight[/C][C]Cosine[/C][C]Optcosine[/C][/ROW]
[ROW][C]Kernel Density Values are not shown[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307252&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307252&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:

Kernel Density Values
x-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')
ab<-table.start()
ab<-table.row.start(ab)
ab<-table.element(ab,'Properties of Density Trace',2,TRUE)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'Bandwidth',header=TRUE)
ab<-table.element(ab,mydensity1$bw)
ab<-table.row.end(ab)
ab<-table.row.start(ab)
ab<-table.element(ab,'#Observations',header=TRUE)
ab<-table.element(ab,mydensity1$n)
ab<-table.row.end(ab)
ab<-table.end(ab)
a <- ab
table.save(ab,file='mytable123.tab')
b<-table.start()
b<-table.row.start(b)
b<-table.element(b,'Maximum Density Values',3,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Kernel',1,TRUE)
b<-table.element(b,'x-value',1,TRUE)
b<-table.element(b,'max. density',1,TRUE)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Gaussian',1,TRUE)
b<-table.element(b,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
b<-table.element(b,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Epanechnikov',1,TRUE)
b<-table.element(b,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
b<-table.element(b,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Rectangular',1,TRUE)
b<-table.element(b,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
b<-table.element(b,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Triangular',1,TRUE)
b<-table.element(b,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
b<-table.element(b,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Biweight',1,TRUE)
b<-table.element(b,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
b<-table.element(b,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Cosine',1,TRUE)
b<-table.element(b,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
b<-table.element(b,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
b<-table.row.end(b)
b<-table.row.start(b)
b<-table.element(b,'Optcosine',1,TRUE)
b<-table.element(b,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
b<-table.element(b,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
b<-table.row.end(b)
b<-table.end(b)
a <- b[1]
table.save(b,file='mytable2a.tab')
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)
if (par2=='yes') {
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)
}
} else {
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values are not shown',8)
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')