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*The author of this computation has been verified*

R Software Module

rwasp_density.wasp

Title produced by software

Kernel Density Estimation

Date of computation

Sat, 17 Nov 2018 19:33:15 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Nov/17/t15424801476uxao9cg36odep3.htm/, Retrieved Sat, 04 May 2024 08:22:09 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 08:22:09 +0200

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User-defined keywords

h=1

Estimated Impact

Dataseries X:

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5.0246058
5.5160598
5.9713376
7.0147872
5.2454103
4.4402254
3.0622244
6.5664193
7.380746
2.1755158
4.899559
6.8111174
3.9808917
6.4306712
3.3760212
5.1110294
2.9217554
7.3493386
10.10077
6.5010265
8.2680059
2.7773663
5.8087998
4.5933366
11.008886
7.7285931
1.9610304
7.6644554
4.2862899
2.248033
6.1024448
6.7368937
2.9785089
4.0621344
5.5120039
5.7096455
6.4148654
6.3900398
10.411563
3.7637522
2.7613122
5.0880036
3.3347784
2.895194
2.5186661
4.0699212
3.8277805
5.649159
5.8182264
2.2966683
3.9808917
1.4928344
2.5683172
5.5953969
10.615711
8.2046853
1.2248898
11.005995
6.6148151
1.5976823
7.1671632
7.655561
4.1513955
9.5983723
6.486178
9.4222289
8.0440522
4.899559
4.899559
4.6584903
3.5092098
1.8423962
3.0696033
3.934781
3.0622244
6.1244488
4.899559
5.3588927
6.250372
3.9808917
5.8644338
4.6350289
1.6193458
5.1644001
3.9282808
4.0867083
6.244536
4.5001385
3.1743397
3.7705169
2.3302781
7.9617834
6.848846
5.1408831
9.5678084
5.8704394
3.9196472
7.655561
6.7368937
4.2871142
8.2104658
2.6429157
3.6746693
0.68982961
1.8219184
6.6494016
3.9808917
2.5022748
1.4868391
4.0969726
7.296718
4.2111912
8.3685899
3.1563066
4.7127233
3.5262163
4.7035767
4.170458
4.8386529
2.4581836
6.1244488
8.8804508
7.655561
5.2025656
3.1546689
3.4198264
4.8859416
0.51979
4.2871142
3.0622244
4.6932618
10.924692
4.6768518
2.4497795
2.2292994
4.2099461
5.1717568
1.2208649
2.920081
2.9098904
1.5589506
3.7688916
7.9617834
0.81659317
3.9502695
2.1710424
4.4585987
3.5486806
11.636453
2.9155827
2.388535
4.899559
7.0431161
4.3871052
5.3078556
5.8941695
2.3306841
1.007024
6.3614749
6.0537661
3.4011502
4.9761146
2.866242
2.7811709
2.7793862
3.1483858
3.6746693
8.8804508
4.899559
0.2813351
7.5564133
4.899559
2.2845864
2.8266687
6.0155697
4.5083711
9.477341
8.6365108
3.6746693
3.122268
9.2007478
4.244108
2.5150747
3.5923014
4.7356333
3.8770424
6.0495647
2.9239909
10.393004
8.593671
7.3175232
7.1628053
6.7691276
6.2195911
11.306675
4.6793541
4.2874353
3.1131118
4.8107453
6.6079579
2.5830213
12.095786
1.446168
7.9617834
5.5885595
5.2182493
3.2168822
3.3291528
3.0622244
4.2747831
4.7464478
6.3422457
1.8355697
5.5941505
2.920081
7.0431161
6.1244488
0.66175862
6.1244488
6.4306712
7.3493386
8.1469412
5.5363283
1.9658159
7.6052857
5.8268055
2.9488087
3.1531816
2.1435571
10.770968
3.1428093
5.1297397
5.4595086
5.5120039
8.3808247
7.1147852
10.105341
10.5654
7.0431161
6.2988793
6.3694268
4.5495905
6.1110613
7.7205173
1.6529654
3.7288588
5.1242371
1.5519415
6.2278839
3.6746693
4.2788855
5.7876041
4.3826331
2.3530366
3.3684468
3.9808917
5.3750437
5.6869882
5.974083
5.2057815
3.3401218
4.4585987
2.8919077
3.6746693
4.432333
2.8999441
3.8572003
7.4189346
6.7368937
4.1159462
8.3510262
11.980796
5.3282705
3.1847134
4.5495905
9.9146737
2.5661
10.781212
6.3141777
2.1435571
9.1947105
2.9010547
1.9231361
5.2057815
0.55120039
5.3978193
10.734989
5.6061305
3.0622244
6.4278619
4.3813552
6.9874556
5.1783957
4.0829659
3.7467216
7.2758802
4.0420289
5.2057815
5.2057815
8.2424532
2.2747953
3.8186012
5.5107716
3.6059544
4.6646781
4.9914258
3.0622244
8.4076433
8.8804508
7.0431161
4.153974
3.5240681
5.3609063
4.1122554
8.5805749
7.4934432
4.5127517
3.4501062
4.3883846
2.4804018
6.3030786
3.8277805
3.461645
3.9546441
8.5379397
5.1205753
2.1435571
3.9479918
3.0534165
4.6443737
2.2579449
9.4528595
6.6625803
10.183676
5.9195416
2.1615702
7.4371955
6.1244488
1.7975805
2.825149
10.105341
6.1244488
6.9596009
7.9950963
6.8900049
5.8107051
7.1764129
1.1921387
3.8956739
3.2899932
3.8743472
4.2685164
6.1143123
3.9844493
8.772984
3.9472504
3.6746693
2.4497795
3.3684468
3.8107681
2.4497795
4.3595188
2.2427559
4.5933366
6.0966805
1.8063296
1.9301293
4.2843678
1.9904459
0.27132808
2.5168968
3.2250262
7.5502925
1.4764709
2.6476239
5.3109506
3.0622244
4.1340029
6.4994151
2.9430717
2.4497795
3.1890621
4.5495905
4.6768518
4.3456128
2.3161552
3.0622244
6.1244488
4.3378616
3.6053359
5.7880389
5.7105205
2.756002
3.3602488
7.2793449
4.8593243
5.1037073
18.515775
5.4712763
5.607929
5.4507594
6.7368937
3.4674434
7.4718275
4.4059193
5.3588927
1.7498425
2.3109031
10.841577
2.756002
3.9808917
3.4253854
1.1942675
3.961299
2.2442611
5.9713376
1.8439201
4.1340029
0.51868296
5.6466549
10.972971
1.0191083
3.7913254
3.0622244
7.0431161
1.9833624
3.1453959
3.3523299
0.55410411
0.32497075
4.4912625
0.55146552
5.7124904
2.4250048
4.5173239
4.6301518
2.3272905
2.1435571
3.6746693
1.481262
1.6761649

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big 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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Properties of Density Trace
Bandwidth	1
#Observations	1569

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 1 \tabularnewline
#Observations & 1569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]1[/C][/ROW]
[ROW][C]#Observations[/C][C]1569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Bandwidth	1
#Observations	1569

Maximum Density Values
Kernel	x-value	max. density
Gaussian	4.06899891385519	0.155194807651785
Epanechnikov	4.21937403866928	0.15610941242331
Rectangular	4.44493672589041	0.161422487542801
Triangular	4.14418647626223	0.155443435703523
Biweight	4.14418647626223	0.155517992708203
Cosine	4.14418647626223	0.155406420441002
Optcosine	4.21937403866928	0.155891056406987

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 4.06899891385519 & 0.155194807651785 \tabularnewline
Epanechnikov & 4.21937403866928 & 0.15610941242331 \tabularnewline
Rectangular & 4.44493672589041 & 0.161422487542801 \tabularnewline
Triangular & 4.14418647626223 & 0.155443435703523 \tabularnewline
Biweight & 4.14418647626223 & 0.155517992708203 \tabularnewline
Cosine & 4.14418647626223 & 0.155406420441002 \tabularnewline
Optcosine & 4.21937403866928 & 0.155891056406987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]4.06899891385519[/C][C]0.155194807651785[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]4.21937403866928[/C][C]0.15610941242331[/C][/ROW]
[ROW][C]Rectangular[/C][C]4.44493672589041[/C][C]0.161422487542801[/C][/ROW]
[ROW][C]Triangular[/C][C]4.14418647626223[/C][C]0.155443435703523[/C][/ROW]
[ROW][C]Biweight[/C][C]4.14418647626223[/C][C]0.155517992708203[/C][/ROW]
[ROW][C]Cosine[/C][C]4.14418647626223[/C][C]0.155406420441002[/C][/ROW]
[ROW][C]Optcosine[/C][C]4.21937403866928[/C][C]0.155891056406987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
Kernel	x-value	max. density
Gaussian	4.06899891385519	0.155194807651785
Epanechnikov	4.21937403866928	0.15610941242331
Rectangular	4.44493672589041	0.161422487542801
Triangular	4.14418647626223	0.155443435703523
Biweight	4.14418647626223	0.155517992708203
Cosine	4.14418647626223	0.155406420441002
Optcosine	4.21937403866928	0.155891056406987

Kernel Density Values
x-value	Gaussian	Epanechnikov	Rectangular	Triangular	Biweight	Cosine	Optcosine
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=&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=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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-value	Gaussian	Epanechnikov	Rectangular	Triangular	Biweight	Cosine	Optcosine
Kernel Density Values are not shown

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = no ; par3 = 512 ;

Parameters (R input):

par1 = 1 ; par2 = no ; par3 = 512 ;

R code (references can be found in the software module):

par3 <- '512'
par2 <- 'no'
par1 <- '0,5'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code