num.arcsPEend.int {pcds}

Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end-interval case

Description

Returns the number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) whose vertices are a 1D numerical data set, Xp, outside the interval int=(a,b).

PE proximity region is constructed only with expansion parameter r \ge 1 for points outside the interval (a,b). End vertex regions are based on the end points of the interval, i.e., the corresponding vertex region is an interval as (-\infty,a) or (b,\infty) for the interval (a,b). For the number of arcs, loops are not allowed, so arcs are only possible for points outside the interval, int, for this function.

See also (Ceyhan (2012)).

Usage

num.arcsPEend.int(Xp, int, r)

Arguments

Xp

A vector of 1D points which constitute the vertices of the digraph.

int

A vector of two real numbers representing an interval.

r

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

Value

Number of arcs for the PE-PCD with vertices being 1D data set, Xp, expansion parameter, r \ge 1, for the 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

num.arcsPEmid.int, num.arcsPE1D, num.arcsCSmid.int, and num.arcsCSend.int

Examples

a<-0; b<-10; int<-c(a,b)

n<-5
XpL<-runif(n,a-5,a)
XpR<-runif(n,b,b+5)
Xp<-c(XpL,XpR)

r<-1.2
num.arcsPEend.int(Xp,int,r)
num.arcsPEend.int(Xp,int,r=2)