funsMuVarPE2D {pcds}

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 (Ceyhan et al. (2006)).

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

Ceyhan E, Priebe CE, Wierman JC (2006). “Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.” Computational Statistics & Data Analysis, 50(8), 1925-1964.

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)