funsMuVarPE2D: Returns the mean and (asymptotic) variance of arc density of...

In pcds: Proximity Catch Digraphs and Their Applications

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 asy.varPE2D.

muPE2D returns the mean of the (arc) density of PE-PCD and asy.varPE2D returns the asymptotic variance of the arc density of PE-PCD for 2D uniform data in a triangle.

PE proximity regions are defined with expansion parameter r \ge 1 with respect to the triangle in which the points reside and vertex regions are based on center of mass, CM of the triangle.

See also (\insertCiteceyhan:arc-density-PE;textualpcds).

Usage

muPE2D(r)

asy.varPE2D(r)

Arguments

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

Value

muPE2D returns the mean and asy.varPE2D returns the (asymptotic) variance of the arc density of PE-PCD for uniform data in any triangle.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

muCS2D and asy.varCS2D

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 asy.varPE2D
asy.varPE2D(1.2)

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

avar<-vector()
for (i in 1:lrseq)
{
  avar<-c(avar,asy.varPE2D(rseq[i]))
}

oldpar <- 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)

pcds documentation built on May 29, 2024, 9:36 a.m.