Free Statistics

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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 computationThu, 31 Jan 2019 10:46:09 +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/2019/Jan/31/t1548927983gm8al41468ohysd.htm/, Retrieved Sun, 05 May 2024 17:20:42 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 17:20:42 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
0.7923
-2.468
-2.996
3.119
0.04315
0.731
2.45
2.119
-1.429
-1.644
-3.065
-1.461
1.141
1.329
0.3396
0.8429
2.225
-1.924
0.4999
-0.6433




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=&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=&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 Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







Properties of Density Trace
Bandwidth0.92091400382747
#Observations20

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.92091400382747 \tabularnewline
#Observations & 20 \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]0.92091400382747[/C][/ROW]
[ROW][C]#Observations[/C][C]20[/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
Bandwidth0.92091400382747
#Observations20







Maximum Density Values
Kernelx-valuemax. density
Gaussian0.8175620328616170.187796278125443
Epanechnikov1.161284655844930.178370590402291
Rectangular-0.3969245683460850.188079538411859
Triangular0.7946471913293960.18452292071722
Biweight1.046710448183820.18017224804631
Cosine0.9779659235871630.180965451602097
Optcosine1.115454972780490.179019452677684

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 0.817562032861617 & 0.187796278125443 \tabularnewline
Epanechnikov & 1.16128465584493 & 0.178370590402291 \tabularnewline
Rectangular & -0.396924568346085 & 0.188079538411859 \tabularnewline
Triangular & 0.794647191329396 & 0.18452292071722 \tabularnewline
Biweight & 1.04671044818382 & 0.18017224804631 \tabularnewline
Cosine & 0.977965923587163 & 0.180965451602097 \tabularnewline
Optcosine & 1.11545497278049 & 0.179019452677684 \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]0.817562032861617[/C][C]0.187796278125443[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]1.16128465584493[/C][C]0.178370590402291[/C][/ROW]
[ROW][C]Rectangular[/C][C]-0.396924568346085[/C][C]0.188079538411859[/C][/ROW]
[ROW][C]Triangular[/C][C]0.794647191329396[/C][C]0.18452292071722[/C][/ROW]
[ROW][C]Biweight[/C][C]1.04671044818382[/C][C]0.18017224804631[/C][/ROW]
[ROW][C]Cosine[/C][C]0.977965923587163[/C][C]0.180965451602097[/C][/ROW]
[ROW][C]Optcosine[/C][C]1.11545497278049[/C][C]0.179019452677684[/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
Kernelx-valuemax. density
Gaussian0.8175620328616170.187796278125443
Epanechnikov1.161284655844930.178370590402291
Rectangular-0.3969245683460850.188079538411859
Triangular0.7946471913293960.18452292071722
Biweight1.046710448183820.18017224804631
Cosine0.9779659235871630.180965451602097
Optcosine1.115454972780490.179019452677684







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=&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-valueGaussianEpanechnikovRectangularTriangularBiweightCosineOptcosine
Kernel Density Values are not shown



Parameters (Session):
par1 = 500121222pearson11111111212120000FALSEFALSE0two.sidedtwo.sided20011two.sided0.010.0250.02520031111111111two.sidedtwo.sided0.850.0251Default124additive1Default11pearson11111111111pearson11110.025200Default1111additive12121212Defaultpearson0 ; par2 = 122111Do not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDoubleTriple11111110.970.975220.850.990.9750.97551Do not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal Dummies0.850.8500.975011201022222Do not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal DummiesInclude Seasonal DummiesDo not include Seasonal DummiesDo not include Seasonal Dummies22Do not include Seasonal DummiesDo not include Seasonal Dummies0.97551000012SingleTripleDoubleTriple1no ; par3 = 5Pearson Chi-SquaredTRUE33No Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear Trendadditiveadditive0000000201503Pearson Chi-Squared00.010.050.0502No Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear Trend000.0500000Exact Pearson Chi-Squared by Simulation0.990.990.990.95No Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear TrendNo Linear Trend33No Linear TrendNo Linear Trend0.05000000additiveadditiveadditiveadditive0512 ; par4 = P1 P5 Q1 Q3 P95 P9912TRUE1212121212121111111P0.5 P2.5 Q1 Q3 P97.5 P99.5TRUEP0.5 P2.5 Q1 Q3 P97.5 P99.5TRUE12121212121212012401212two.sided12two.sided1TRUETRUEP0.5 P2.5 Q1 Q3 P97.5 P99.501111121212120 ; par5 = 121212121212121212unpairedunpairedunpairedunpaired11212 ; par6 = 12121212121212333333312121212121212121212112White NoiseWhite Noise000121212121212121212White NoiseWhite Noise ; par7 = 11221110.950.950.950.95 ; par8 = 1021211 ; par9 = 1111110 ; par10 = FALSEFALSEFALSEFALSEFALSE ;
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')