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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 computationSat, 13 Dec 2014 10:06:25 +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/13/t1418465215kj6xmxsadhx75tx.htm/, Retrieved Fri, 01 Nov 2024 00:11:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=266934, Retrieved Fri, 01 Nov 2024 00:11:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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] [Gaussian kernel LFM] [2014-12-13 10:06:25] [d0ee3c98d5e00815b38c7c808f1992f4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
149
139
148
158
128
224
159
105
159
167
165
159
119
176
54
91
163
124
137
121
153
148
221
188
149
244
148
92
150
153
94
156
132
161
105
97
151
131
166
157
111
145
162
163
59
187
109
90
105
83
116
42
148
155
125
116
128
138
49
96
164
162
99
202
186
66
183
214
188
104
177
126
76
99
139
162
108
159
74
110
96
116
87
97
127
106
80
74
91
133
74
114
140
95
98
121
126
98
95
110
70
102
86
130
96
102
100
94
52
98
118
99
48
50
150
154
109
68
194
158
159
67
147
39
100
111
138
101
131
101
114
165
114
111
75
82
121
32
150
117
71
165
154
126
149
145
120
109
132
172
169
114
156
172
68
89
167
113
115
78
118
87
173
2
162
49
122
96
100
82
100
115
141
165
165
110
118
158
146
49
90
121
155
104
147
110
108
113
115
61
60
109
68
111
77
73
151
89
78
110
220
65
141
117
122
63
44
52
131
101
42
152
107
77
154
103
96
175
57
112
143
49
110
131
167
56
137
86
121
149
168
140
88
168
94
51
48
145
66
85
109
63
102
162
86
114
164
119
126
132
142
83
94
81
166
110
64
93
104
105
49
88
95
102
99
63
76
109
117
57
120
73
91
108
105
117
119

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266934&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266934&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Properties of Density Trace
Bandwidth11.5649266944683
#Observations277

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 11.5649266944683 \tabularnewline
#Observations & 277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266934&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]11.5649266944683[/C][/ROW]
[ROW][C]#Observations[/C][C]277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266934&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
Bandwidth11.5649266944683
#Observations277






Maximum Density Values
Kernelx-valuemax. density
Gaussian106.8516177212910.0106213187898442
Epanechnikov107.4609906374680.0104428965212728
Rectangular101.9766343918690.0104303540566488
Triangular108.6797364698240.0104856301213974
Biweight106.8516177212910.0104874154427853
Cosine106.8516177212910.0105019091102532
Optcosine107.4609906374680.0104613029315296

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 106.851617721291 & 0.0106213187898442 \tabularnewline
Epanechnikov & 107.460990637468 & 0.0104428965212728 \tabularnewline
Rectangular & 101.976634391869 & 0.0104303540566488 \tabularnewline
Triangular & 108.679736469824 & 0.0104856301213974 \tabularnewline
Biweight & 106.851617721291 & 0.0104874154427853 \tabularnewline
Cosine & 106.851617721291 & 0.0105019091102532 \tabularnewline
Optcosine & 107.460990637468 & 0.0104613029315296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=266934&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]106.851617721291[/C][C]0.0106213187898442[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]107.460990637468[/C][C]0.0104428965212728[/C][/ROW]
[ROW][C]Rectangular[/C][C]101.976634391869[/C][C]0.0104303540566488[/C][/ROW]
[ROW][C]Triangular[/C][C]108.679736469824[/C][C]0.0104856301213974[/C][/ROW]
[ROW][C]Biweight[/C][C]106.851617721291[/C][C]0.0104874154427853[/C][/ROW]
[ROW][C]Cosine[/C][C]106.851617721291[/C][C]0.0105019091102532[/C][/ROW]
[ROW][C]Optcosine[/C][C]107.460990637468[/C][C]0.0104613029315296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=266934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=266934&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
Gaussian106.8516177212910.0106213187898442
Epanechnikov107.4609906374680.0104428965212728
Rectangular101.9766343918690.0104303540566488
Triangular108.6797364698240.0104856301213974
Biweight106.8516177212910.0104874154427853
Cosine106.8516177212910.0105019091102532
Optcosine107.4609906374680.0104613029315296


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')
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')
}