funsMuVarPEend.int {pcds}

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: muPEend.int and asy.varPEend.int.

muPEend.int returns the mean of the arc density of PE-PCD and asy.varPEend.int 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 (2012)).

Usage

muPEend.int(r)

asy.varPEend.int(r)

Arguments

r

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

Value

muPEend.int returns the mean and asy.varPEend.int returns the asymptotic variance of the arc density of PE-PCD for uniform data in end-intervals

Author(s)

Elvan Ceyhan

References

Ceyhan E (2012). “The Distribution of the Relative Arc Density of a Family of Interval Catch Digraph Based on Uniform Data.” Metrika, 75(6), 761-793.

See Also

muCSend.int and asy.varCSend.int

Examples

#Examples for muPEend.int
muPEend.int(1.2)

rseq<-seq(1.01,5,by=.1)
lrseq<-length(rseq)

mu.end<-vector()
for (i in 1:lrseq)
{
  mu.end<-c(mu.end,muPEend.int(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 asy.varPEend.int
asy.varPEend.int(1.2)

rseq<-seq(1.01,5,by=.1)
lrseq<-length(rseq)

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

oldpar <- 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)