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Author*The author of this computation has been verified*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationThu, 21 Dec 2017 21:55:44 +0100
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/Dec/21/t1513889842qshq0mhrek1h34l.htm/, Retrieved Tue, 14 May 2024 09:50:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310725, Retrieved Tue, 14 May 2024 09:50:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Kernel Density Estimation] [Totale Belastinge...] [2017-12-21 20:55:44] [f7fcbef48f036f8c57e773abb9891403] [Current]
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Dataseries X:
83674204.92
1780582985.50
75198229.43
66552858.02
47377292.82
202450191.48
139917216.59
129019740.35
70169361.12
49375016.78
59073785.95
89062635.98
149805035.68
121657356.12
53218003.32
134314180.33
41501724.73
101190684.88
78601349.78
41458023.49
124456725.54
175844207.75
95041211.77
47068781.84
60350058.62
85555510.86
64400011.97
116681743.38
88648506.56
69194523.37
51115705.16
100175600.31
111989704.69
87312371.62
189344006.44
164413751.73
389423515.99
102126834.31
82120289.65
90980789.21
41278167.54
108959432.50
110751384.31
45096581.99
5530000.01
91412977.98
82847784.50
36612438.99
181071513.72
53746879.90
124559250.64
36698020.15
62934778.95
73414447.19
45884687.67
87832898.47
73069485.61
42195466.42
35830154.17
156770436.11
54294999.18
58513045.36
43527242.04
43205602.28
44706884.64
160914168.27
35082993.05
59822334.79
112211208.73
65205148.09
238077836.32
165219181.12
86130405.49
461964651.71
171139517.93
111032333.28
180249086.05
77894859.75
356473658.26
166542522.62
54125197.52
168151470.10
135764498.43
37570670.97
315804194.31
423707340.96
135714858.80
243733834.55
237163226.09
161036493.87
143348790.49
10888021.53
237468586.59
46198566.04
51437155.59
209130115.72
176879819.50
35045038.21
65096793.73
73508446.84
51708403.59
58292306.49
102123580.00
53158301.57
124494225.89
91583660.26
76281205.42
163529644.28
26774034.54
144704279.83
69114646.47
86950644.80
175990756.79
158929908.10
148155746.78
62779862.12
19818260.44
88601705.01
30007930.38
117832980.18
90848930.71
89397843.03
55263706.65
69991137.65
143797027.39
52673003.03
28706022.10
62998324.49
67833116.68
75723475.10
48325193.00
111360028.58
24660326.90
82460584.67
145281782.55
39486520.21
60947767.64
60121930.24
99017214.81
35238165.30
123420536.16
74746463.17
562343449.26
94683693.97
81904382.19
99095998.96
142175940.20
155903769.11
78634994.57
36977845.61
34414962.16
102341645.98
56237645.75
27172686.96
41273198.60
216175606.08
55898647.10
75221385.94
53676891.83
81091784.87
77042398.81
28174938.67
35101461.83
68538574.63
44615475.28
43069115.58
143983064.34
46825971.36
134566048.14
90240422.37
56049938.72
175425686.55
176518866.51
40669236.13
15735297.80
98139206.91
41803620.00
158877910.97
30399756.30
47388802.69
41728417.19
69231928.02
71853610.07
558959084.34
52566146.36
71674599.90
110358574.86
84597608.62
101107225.10
13370105.37
194211934.95
57318082.47
32536505.48
30275241.72
43088560.58
10752495.01
134197141.73
2050754.56
65419855.94
61175707.93
45614657.12
23662737.25
27092741.28
11126014.61
65593377.32
37809417.15
50054204.29
110486000.24
325943399.04
49870777.29
23695745.49
108184247.16
164542311.66
125549650.35
107449263.65
8393570.83
72757794.21
48819423.37
50421429.43
68645643.01
263997474.96
37709829.83
58817989.39
41975398.72
41109010.86
108335047.35
34635284.88
34146816.44
40027824.91
255413911.10
39327036.60
34338165.77
40263957.24
29123563.03
25270133.49
21427131.27
83583036.21
37173439.19
55380715.77
33827105.84
15154155.13
37461595.38
127294245.12
43078336.44
42758206.49
383900334.78
87822482.33
141180713.72
90298133.84
86505418.31
90694450.78
167910891.25
50607613.62
135425474.89
102720180.37
66857581.76
73816862.43
207318845.32
99802773.49
67851606.53
86801450.06
61288989.68
113177815.47
54967014.24
81001444.77
62918316.25
79742451.05
29333512.89
94972892.77
26549874.17
47579300.90
105920074.84
150747468.10
77872467.76
105931079.33
167937296.54
67982977.64
1127522650.64
33917970.01
122322917.57
51191129.67
62534355.27
147382680.51
29776722.78
62470751.06
62340306.49
76224265.73
70626921.41
34032560.79
34234210.43
38939478.00
70303064.10
42727099.37
147403937.87
76803541.00
35977424.43
66205410.90
28025110.03
33531833.06
10151610.61
31918395.56
31383005.56
42887668.11
236404571.67
78960632.59
175788801.46
91832230.46
306046912.37
78331944.89
131983592.11
120919736.51
48935304.19
38373571.39
13482490.40
26820678.58
24159621.41
15019293.19
44094415.15
43221355.88
472963673.61
84489770.96
92558087.82
19273066.83
71065080.27
53076402.93
63601168.39
62866732.28
52874069.45
77463960.29
51942683.95
34252330.78
48107684.67
48876597.95
47073139.89
64901297.63
20289119.53
55054846.84
17940235.70
334072416.20
44388206.89
18310249.52
83896494.88
45722559.76
21836599.30
35118855.23
150765293.54
42201875.01
92723742.48
64474835.50
216962470.14
64400374.43
37629453.81
41434942.09
107382240.34
43023288.68
33909234.14
24467489.05
103834428.13
28659746.45
27671595.46
10962990.77
25238585.05
14135312.91
12952681.63
63439160.04
30006711.39
76152933.75
57222458.69
15673507.41
23649020.47
20416603.84
29797853.38
18958200.07
52901004.30
17401244.28
247393964.80
27080730.38
50451316.51
14470807.48
50823410.95
16614593.12
19358791.49
20497331.08
14199402.87
24633296.00
77518810.76
23520963.94
19995502.56
36034129.65
11122663.82
21201785.37
30503260.49
60550877.27
20320083.81
18597081.06
13308985.77
97603695.92
41843004.31
47124618.11
34820600.19
40156382.31
124578471.31
18582757.50
34038496.74
71144154.14
58098157.86
106321597.38
41691766.42
610101644.52
90944470.74
55309626.74
166135384.26
67216592.50
72174542.68
65801713.92
64816227.13
62085580.91
83483908.03
62917735.31
34295119.05
13574588.68
17416253.17
17727082.01
13431085.51
15172534.44
32540943.64
68775834.47
75444608.45
40462339.40
20772249.10
12345912.81
20373311.51
16455535.66
41430238.43
22237504.51
34029916.05
21232392.13
25249850.80
37982401.65
25217298.61
13068829.57
54488407.77
153120189.19
22855597.19
36810206.96
8419073.01
5730916.51
27858675.43
26261553.11
14590398.03
29541770.29
16371957.79
16291258.87
15857207.06
17038776.18
74697561.03
15452944.58
16912129.43
29259761.68
25248097.12
65919010.85
12207281.77
20251395.73
33416732.62
159605911.86
85079503.42
210834140.85
37364693.10
40564843.01
373521155.87
56683585.68
55883410.76
65487353.48
27817774.15
39922107.66
166458725.96
82156772.62
92996093.99
30743914.40
43275684.47
118542707.01
40563761.39
55855949.38
33426012.30
115874023.29
83855415.36
56925213.51
51740733.34
61084521.87
36774358.09
44711837.49
98317957.16
47860971.78
64488518.70
53036656.78
126762831.05
43174170.46
27015027.09
377094.66
39780669.38
38430137.95
79391438.56
55962069.52
123858678.91
30871857.27
101837566.51
12492775.95
60644882.76
10761253.54
19468295.42
2581083.89
12003062.33
33355567.04
8548450.87
4352375.82
14097650.14
22182800.06
12568081.02
10751225.95
6192572.47
36480577.72
10643018.21
17256072.97
11217260.51
60230572.58
18626805.04
8143091.44
8868805.11
12081820.83
24543956.74
15324447.45
4029081.46
4508075.47
11215550.35
16978476.17
19877893.21
15024577.84
17849749.24
8642730.53
9848011.81
36834521.18
13620030.75
12365667.12
15223219.31
7789669.15
7466085.12
6976990.54
10294001.25
29128119.83
17566176.81
5291185.49
25925453.45
27495855.35
9232653.29
60779131.03
44433224.98
13931267.71
30661156.64
18623146.14
16539661.47
11536267.35
42275408.79
19488550.80
41853937.29
14800207.11
6850020.18
93057221.42
35630707.07
78547195.23
36872176.19
41340222.51
35522149.25
53223208.40
476285852.47
19876445.65
58674083.89
36952141.39
90502312.85
39352343.78
71925661.24
51024382.09
129304683.64
16456921.89
38822191.84
8658219.76
39750993.31
30368830.19
76371351.34
15554523.77




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310725&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310725&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310725&T=0

As an alternative you can also use a 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 time3 seconds
R ServerBig Analytics Cloud Computing Center







Properties of Density Trace
Bandwidth11265002.4402725
#Observations589

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 11265002.4402725 \tabularnewline
#Observations & 589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310725&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]11265002.4402725[/C][/ROW]
[ROW][C]#Observations[/C][C]589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310725&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310725&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth11265002.4402725
#Observations589







Maximum Density Values
Kernelx-valuemax. density
Gaussian35286827.46472281.06741340468499e-08
Epanechnikov31670788.5107471.07930691339427e-08
Rectangular31670788.5107471.15480549454087e-08
Triangular35286827.46472281.0762639447055e-08
Biweight31670788.5107471.07236670716957e-08
Cosine31670788.5107471.07040861020056e-08
Optcosine31670788.5107471.07605448901034e-08

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 35286827.4647228 & 1.06741340468499e-08 \tabularnewline
Epanechnikov & 31670788.510747 & 1.07930691339427e-08 \tabularnewline
Rectangular & 31670788.510747 & 1.15480549454087e-08 \tabularnewline
Triangular & 35286827.4647228 & 1.0762639447055e-08 \tabularnewline
Biweight & 31670788.510747 & 1.07236670716957e-08 \tabularnewline
Cosine & 31670788.510747 & 1.07040861020056e-08 \tabularnewline
Optcosine & 31670788.510747 & 1.07605448901034e-08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310725&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]35286827.4647228[/C][C]1.06741340468499e-08[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]31670788.510747[/C][C]1.07930691339427e-08[/C][/ROW]
[ROW][C]Rectangular[/C][C]31670788.510747[/C][C]1.15480549454087e-08[/C][/ROW]
[ROW][C]Triangular[/C][C]35286827.4647228[/C][C]1.0762639447055e-08[/C][/ROW]
[ROW][C]Biweight[/C][C]31670788.510747[/C][C]1.07236670716957e-08[/C][/ROW]
[ROW][C]Cosine[/C][C]31670788.510747[/C][C]1.07040861020056e-08[/C][/ROW]
[ROW][C]Optcosine[/C][C]31670788.510747[/C][C]1.07605448901034e-08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310725&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310725&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian35286827.46472281.06741340468499e-08
Epanechnikov31670788.5107471.07930691339427e-08
Rectangular31670788.5107471.15480549454087e-08
Triangular35286827.46472281.0762639447055e-08
Biweight31670788.5107471.07236670716957e-08
Cosine31670788.5107471.07040861020056e-08
Optcosine31670788.5107471.07605448901034e-08







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=310725&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=310725&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310725&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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



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')
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')