funsMuVarCSend.int {pcds}

Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case

Description

Two functions: muCSend.int and asy.varCSend.int.

muCSend.int returns the mean of the arc density of CS-PCD and asy.varCSend.int returns the asymptotic variance of the arc density of CS-PCD for a given expansion parameter t>0 for 1D uniform data in the left and right end-intervals for the interval (a,b).

See also (Ceyhan (2016)).

Usage

muCSend.int(t)

asy.varCSend.int(t)

Arguments

t

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

Details

funsMuVarCSend.int

Value

muCSend.int returns the mean and asy.varCSend.int returns the asymptotic variance of the arc density of CS-PCD for uniform data in end-intervals

Author(s)

Elvan Ceyhan

References

Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.

See Also

muPEend.int and asy.varPEend.int

Examples

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

tseq<-seq(0.01,5,by=.05)
ltseq<-length(tseq)

mu.end<-vector()
for (i in 1:ltseq)
{
  mu.end<-c(mu.end,muCSend.int(tseq[i]))
}

oldpar <- par(no.readonly = TRUE)
par(mar = c(5,4,4,2) + 0.1)
plot(tseq, mu.end,type="l",
ylab=expression(paste(mu,"(t)")),xlab="t",lty=1,xlim=range(tseq),ylim=c(0,1))
par(oldpar)

#Examples for asy.varCSend.int
asy.varCSend.int(1.2)

tseq<-seq(.01,5,by=.05)
ltseq<-length(tseq)

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

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