funsMuVarPEend1D: Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end interval case

Description

Two functions: muPEend1D and asyvarPEend1D.

muPEend1D returns the mean of the arc density of PE-PCD and asyvarPEend1D returns the asymptotic variance of the arc density of PE-PCD for a given expansion parameter \(r \ge 1\) for 1D uniform data in the left and right end intervals for the interval \((a,b)\).

See also (ceyhan:metrika-2012;textualpcds).

Usage

muPEend1D(r)
asyvarPEend1D(r)

Arguments

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

Value

muPEend1D returns the mean and asyvarPEend1D returns the asymptotic variance of the arc density of PE-PCD for uniform data in end intervals

References

Examples

Run this code

# NOT RUN {
#Examples for muPEend1D
muPEend1D(1.2)

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

mu.end<-vector()
for (i in 1:lrseq)
{
  mu.end<-c(mu.end,muPEend1D(rseq[i]))
}

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

#Examples for asyvarPEend1D
asyvarPEend1D(1.2)

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

var.end<-vector()
for (i in 1:lrseq)
{
  var.end<-c(var.end,asyvarPEend1D(rseq[i]))
}

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

# }