IarcCSint {pcds}

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

Description

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

CS 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 (2016)).

Usage

IarcCSint(p1, p2, int, t, 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.

t

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

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_{CS}(p_1,t,c)) for p2, that is, returns 1 if p_2 in N_{CS}(p_1,t,c), 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, IarcCSend.int and IarcPEint

Examples

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

IarcCSint(7,5,int,t,c)
IarcCSint(17,17,int,t,c)
IarcCSint(15,17,int,t,c)
IarcCSint(1,3,int,t,c)

IarcCSint(-17,17,int,t,c)

IarcCSint(3,5,int,t,c)
IarcCSint(3,3,int,t,c)
IarcCSint(4,5,int,t,c)
IarcCSint(a,5,int,t,c)

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

IarcCSint(7,5,int,t,c)