Kernel Density Estimation - Free Statistics and Forecasting Software (Calculators) v.1.2.1

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) performs the Kernel Density Estimation for any data series according to the following Kernels: Gaussian, Epanechnikov, Rectangular, Triangular, Biweight, Cosine, and Optcosine. The result is displayed in a series of images.

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Data [reset data]
3850 3900 3900 3950 3950 3900 3400 2150 3800 3950 3950 3850 3750 3900 3850 3900 3900 4000 3450 2300 3900 4100 4150 4150 3950 4150 4150 4150 4150 4250 3750 2350 4200 4250 4350 4300 4150 4250 4250 4200 4150 4350 3750 2450 4250 4350 4450 4500 4350 4500 4550 4550 3050 3850 4100 2700 4450 4800 4950 4950 4800 4850 4850 5000 5000 5000 4450 2800 4850 5150 5050 5100 5100 5250 5250 5350 5150 5200 4600 2950 5100 5350 5350 5400 5250 5450 5500 5450 5200 5400 4800 3050 5450 5600 5750 5750 5650 5700 5750 5800 5750 5750 4950 3500 5750 6050 6150 6200 6150 6250 6300 6100 6350 6250 5400 3900 6100 6450 6600 6350 6500 6700 6550 6550 6550 6500


Sample Range: (leave blank to include all observations)
From:
To:

Smoothing Bandwidth (leave zero for default)


Display values (?)


Number of density points (?)


Chart options
Width:
Height:
Label y-axis:
Label x-axis:

Source code of R 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")

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:: Kernel Density Estimation - Free Statistics Software (Calculator) ::