IarcCSend.int {pcds}

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case

Description

Returns I(p_2 in N_{CS}(p_1,t)) for points p_1 and p_2, that is, returns 1 if p_2 is in N_{CS}(p_1,t), returns 0 otherwise, where N_{CS}(x,t) is the CS proximity region for point x with expansion parameter t>0 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 (2016)).

Usage

IarcCSend.int(p1, p2, int, t, rv = NULL)

Arguments

p1

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

p2

A 1D point to check whether it is inside the proximity region or not.

int

A vector of two real numbers representing an interval.

t

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

rv

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

Value

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

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

IarcCSmid.int, IarcPEmid.int, and IarcPEend.int

Examples

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

IarcCSend.int(15,17,int,t)
IarcCSend.int(15,15,int,t)

IarcCSend.int(1.5,17,int,t)
IarcCSend.int(1.5,1.5,int,t)

IarcCSend.int(-15,17,int,t)

IarcCSend.int(-15,-17,int,t)

a<-0; b<-10; int<-c(a,b)
t<-.5

IarcCSend.int(15,17,int,t)