funsMuVarCS2D {pcds}

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 asy.varCS2D.

muCS2D returns the mean of the (arc) density of CS-PCD and asy.varCS2D 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 (2005); Ceyhan et al. (2007)).

Usage

muCS2D(t)

asy.varCS2D(t)

Arguments

t

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

Value

muCS2D returns the mean and asy.varCS2D returns the (asymptotic) variance of the arc density of CS-PCD for uniform data in any triangle

Author(s)

Elvan Ceyhan

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

See Also

muPE2D and asy.varPE2D

Examples

#Examples for muCS2D
muCS2D(.5)

tseq<-seq(0.01,5,by=.1)
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 asy.varCS2D
asy.varCS2D(.5)

tseq<-seq(0.01,10,by=.1)
ltseq<-length(tseq)

asy.var<-vector()
for (i in 1:ltseq)
{
  asy.var<-c(asy.var,asy.varCS2D(tseq[i]))
}

oldpar <- par(mar=c(5,5,4,2))
plot(tseq, asy.var,type="l",xlab="t",
    ylab=expression(paste(sigma^2,"(t)")),lty=1,xlim=range(tseq))
par(oldpar)