pcds (version 0.1.4)

funsMuVarPE2D: Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D uniform data in one triangle

Description

Two functions: muPE2D and asyvarPE2D.

muPE2D returns the mean of the (arc) density of PE-PCD and asyvarPE2D returns the asymptotic variance of the arc density of PE-PCD with expansion parameter \(r \ge 1\) for 2D uniform data in a triangle.

PE 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:arc-density-PE;textualpcds).

Usage

muPE2D(r)
asyvarPE2D(r)

Value

muPE2D returns the mean and asyvarPE2D returns the (asymptotic) variance of the arc density of PE-PCD for uniform data in any triangle

Arguments

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

Author

Elvan Ceyhan

References

See Also

muCS2D and asyvarCS2D

Examples

#Examples for muPE2D
muPE2D(1.2)

rseq<-seq(1.01,5,by=.05)
lrseq<-length(rseq)

mu<-vector()
for (i in 1:lrseq)
{
  mu<-c(mu,muPE2D(rseq[i]))
}

plot(rseq, mu,type="l",xlab="r",ylab=expression(mu(r)),lty=1,xlim=range(rseq),ylim=c(0,1))

#Examples for asyvarPE2D
asyvarPE2D(1.2)

rseq<-seq(1.01,5,by=.05)
lrseq<-length(rseq)

avar<-vector()
for (i in 1:lrseq)
{
  avar<-c(avar,asyvarPE2D(rseq[i]))
}

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