funsMuVarCS2D {pcds} | R Documentation |
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)).
muCS2D(t)
asy.varCS2D(t)
t |
A positive real number which serves as the expansion parameter in CS proximity region. |
muCS2D
returns the mean and asy.varCS2D
returns the (asymptotic) variance of the
arc density of CS-PCD for uniform data in any triangle
Elvan Ceyhan
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.
muPE2D
and asy.varPE2D
#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)