IarcPEend.int {pcds}

The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end-interval case

Description

Returns I(p_2 \in N_{PE}(p_1,r)) for points p_1 and p_2, that is, returns 1 if p_2 is in N_{PE}(p_1,r), returns 0 otherwise, where N_{PE}(x,r) is the PE proximity region for point x with expansion parameter r \ge 1 for the region outside the interval (a,b).

rv is the index of the end vertex region p_1 resides, with default=NULL, and rv=1 for left end-interval and rv=2 for the right end-interval. If p_1 and p_2 are distinct and either of them are inside interval int, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

See also (Ceyhan (2012)).

Usage

IarcPEend.int(p1, p2, int, r, rv = NULL)

Arguments

p1

A 1D point whose PE proximity region is constructed.

p2

A 1D point. The function determines whether p_2 is inside the PE proximity region of p_1 or not.

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.

rv

Index of the end-interval containing the point, either 1,2 or NULL (default is NULL).

Value

I(p_2 \in N_{PE}(p_1,r)) for points p_1 and p_2, that is, returns 1 if p_2 is in N_{PE}(p_1,r) (i.e., if there is an arc from p_1 to p_2), returns 0 otherwise

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

IarcPEmid.int, IarcCSmid.int, and IarcCSend.int

Examples

a<-0; b<-10; int<-c(a,b)
r<-2

IarcPEend.int(15,17,int,r)
IarcPEend.int(1.5,17,int,r)
IarcPEend.int(-15,17,int,r)