IarcPEint {pcds}

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

Description

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

PE proximity region is constructed with respect to the interval (a,b). This function works whether p_1 and p_2 are inside or outside the interval int.

Vertex regions for middle intervals are based on the center associated with the centrality parameter c \in (0,1). If p_1 and p_2 are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph).

See also (Ceyhan (2012)).

Usage

IarcPEint(p1, p2, int, r, c = 0.5)

Arguments

p1

A 1D point for which the proximity region is constructed.

p2

A 1D point for which it is checked whether it resides in the 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.

c

A positive real number in (0,1) parameterizing the center inside int=(a,b) with the default c=.5. For the interval, int=(a,b), the parameterized center is M_c=a+c(b-a).

Value

I(p_2 \in N_{PE}(p_1,r,c)), that is, returns 1 if p_2 in N_{PE}(p_1,r,c), 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, IarcPEend.int and IarcCSint

Examples

c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)

IarcPEint(7,5,int,r,c)
IarcPEint(15,17,int,r,c)
IarcPEint(1,3,int,r,c)