pcds (version 0.1.4)

funsMuVarCS2D: Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 2D uniform data in one triangle

Description

Two functions: muCS2D and asyvarCS2D.

muCS2D returns the mean of the (arc) density of CS-PCD and asyvarCS2D returns the asymptotic variance of the arc density of CS-PCD with expansion parameter \(t>0\) for 2D uniform data in a triangle.

CS proximity regions are defined with respect to the triangle and vertex regions are based on center of mass, \(CM\) of the triangle.

See also (ceyhan:Phd-thesis,ceyhan:arc-density-CS;textualpcds).

Usage

muCS2D(t)
asyvarCS2D(t)

Value

muCS2D returns the mean and asyvarCS2D returns the (asymptotic) variance of the arc density of CS-PCD for uniform data in any triangle

Arguments

t

A positive real number which serves as the expansion parameter in CS proximity region.

Author

Elvan Ceyhan

References

See Also

muPE2D and asyvarPE2D

Examples

#Examples for muCS2D
muCS2D(.5)

tseq<-seq(0.01,5,by=.05)
ltseq<-length(tseq)

mu<-vector()
for (i in 1:ltseq)
{
  mu<-c(mu,muCS2D(tseq[i]))
}

plot(tseq, mu,type="l",xlab="t",ylab=expression(mu(t)),lty=1,xlim=range(tseq))

#Examples for asyvarCS2D
asyvarCS2D(.5)

tseq<-seq(0.01,10,by=.05)
ltseq<-length(tseq)

asyvar<-vector()
for (i in 1:ltseq)
{
  asyvar<-c(asyvar,asyvarCS2D(tseq[i]))
}

oldpar <- par(no.readonly = TRUE)
par(mar=c(5,5,4,2))
plot(tseq, asyvar,type="l",xlab="t",ylab=expression(paste(sigma^2,"(t)")),lty=1,xlim=range(tseq))
par(oldpar)