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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationWed, 17 Dec 2014 14:46:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418827570qyaugz23kqnuqkb.htm/, Retrieved Thu, 16 May 2024 13:51:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270354, Retrieved Thu, 16 May 2024 13:51:23 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Survey Scores] [Summary Mean Vs. ...] [2014-12-15 09:53:50] [69bf0eb8b9b38defaaf4848d8c317571]
- RMPD    [Kernel Density Estimation] [] [2014-12-17 14:46:01] [7de19aadd459682308988067914fc05d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
76
119
119
91
138
97
117
125
95
168
109
115
135
130
131
143
134
109
126
117
155
136
132
129
129
131
123
125
112
131
129
99
114
128
130
112
122
115
124
120
119
123
91
107
118
111
95
135
108
130
143
110
131
113
103
140
125
127
116
120
108
111
125
126
116
104
113
106
139
119
112
101
110
115
116
122
111
115
112
109
97
132
102
124
115
128
121
130
99
122
126
141
124
127
114
99
137
97
108
138
123
125
106
138
127
142
94
133
119
114
114
123
126
118
132
127
103
72
113
125
109
111
105
122
127
117
91
143
116
123
101
119
143
114
108
128
122
133
94
128
108
125
130
112
89
117
142
128
114
123
89
125
110
112
109
108
139
116
116
88
128
125
134
126
121
106
109
127
101
120
99
116
125
121
127
129
155
113
125
114
116
127
102
87
110
115
108
97
119
130
97
120
125
131
129
125
108
142
117
130
93
97
120
110
111
130
66
113
126
114
130
112
126
86
122
118
124
120
128
134
133
131
102
97
93
129
115
116
136
142
112
120
121
110
122
133
136
118
130
114
147
123
121
119
129
137
63
134
140
134
121
105
114
106
135
100
101
131
131
129
120
117
82
106
125
130
147
125
97
101
128
97
126
118
107
87
156
133
132
133
122
125
127
125
99
128
110
127
99
126
98
120
118
121
121
118
53
121
111
117
107
129
100
114
122
120
132
107
117
110
129
114
121
123
131
122
118
103
108
95
116
131
106
132
124
114
139
106
106
135
106
113
119
130
139
104
117
132
124
102
121
96
134
122
152
112
115
120
116
141
137
106
128
91
112
140
132
107
124
105
114
112
113
137
103
122
121
123
126
108
129
101
115
143
111
115
138
126
140
122
112
137
114
134
125
106
135
133
146
124
109
127
128
128
147
132
118
128
100
111
132
138
149
114
125
114
105
137
137
103
118
104
135
121
128
140
92
145
130
102
116
118
131
109
139
104
112
131
75
109
117
101
141
114
124
117
103
106
128
130
130
136
127
131
120
126
130
99
140
130
161
118
121
139
102
118
120
129
104
104
111
135
136
110
129
125
128
140
145
138
130
148
77
132
113
128
136
110
116
128
155
73
120
126
133
142
117
108
142
125
112
103
134
121
117
128
135
124

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270354&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]3 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=270354&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270354&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Properties of Density Trace
Bandwidth3.83053065694265
#Observations498

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 3.83053065694265 \tabularnewline
#Observations & 498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270354&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]3.83053065694265[/C][/ROW]
[ROW][C]#Observations[/C][C]498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270354&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270354&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
Bandwidth3.83053065694265
#Observations498






Maximum Density Values
Kernelx-valuemax. density
Gaussian126.2965093162170.0275666281891955
Epanechnikov124.9463803148310.0275046490235175
Rectangular123.5962513134450.0287610277101853
Triangular125.2164061151080.0275263783275581
Biweight125.4864319153850.0274777957959498
Cosine125.7564577156630.0274771370798531
Optcosine125.2164061151080.0274831417921308

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 126.296509316217 & 0.0275666281891955 \tabularnewline
Epanechnikov & 124.946380314831 & 0.0275046490235175 \tabularnewline
Rectangular & 123.596251313445 & 0.0287610277101853 \tabularnewline
Triangular & 125.216406115108 & 0.0275263783275581 \tabularnewline
Biweight & 125.486431915385 & 0.0274777957959498 \tabularnewline
Cosine & 125.756457715663 & 0.0274771370798531 \tabularnewline
Optcosine & 125.216406115108 & 0.0274831417921308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270354&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]126.296509316217[/C][C]0.0275666281891955[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]124.946380314831[/C][C]0.0275046490235175[/C][/ROW]
[ROW][C]Rectangular[/C][C]123.596251313445[/C][C]0.0287610277101853[/C][/ROW]
[ROW][C]Triangular[/C][C]125.216406115108[/C][C]0.0275263783275581[/C][/ROW]
[ROW][C]Biweight[/C][C]125.486431915385[/C][C]0.0274777957959498[/C][/ROW]
[ROW][C]Cosine[/C][C]125.756457715663[/C][C]0.0274771370798531[/C][/ROW]
[ROW][C]Optcosine[/C][C]125.216406115108[/C][C]0.0274831417921308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270354&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270354&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
Gaussian126.2965093162170.0275666281891955
Epanechnikov124.9463803148310.0275046490235175
Rectangular123.5962513134450.0287610277101853
Triangular125.2164061151080.0275263783275581
Biweight125.4864319153850.0274777957959498
Cosine125.7564577156630.0274771370798531
Optcosine125.2164061151080.0274831417921308


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')
}