IarcCSmid.int {pcds}

The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle 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 and is constructed with expansion parameter t>0 and centrality parameter c \in (0,1) for the interval (a,b).

CS proximity regions are defined with respect to the middle interval int and vertex regions are based on the center associated with the centrality parameter c \in (0,1). For the interval, int=(a,b), the parameterized center is M_c=a+c(b-a). rv is the index of the vertex region p_1 resides, with default=NULL.

If p_1 and p_2 are distinct and either of them are outside interval int, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph).

See also (Ceyhan (2016)).

Usage

IarcCSmid.int(p1, p2, int, t, c = 0.5, rv = NULL)

Arguments

p1, p2

1D points; p_1 is the point for which the proximity region, N_{CS}(p_1,t,c) is constructed and p_2 is the point which the function is checking whether its inside N_{CS}(p_1,t,c) 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).

rv

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

Value

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

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

IarcCSend.int, IarcPEmid.int, and IarcPEend.int

Examples

c<-.5
t<-2
a<-0; b<-10; int<-c(a,b)

IarcCSmid.int(7,5,int,t,c)
IarcCSmid.int(7,7,int,t,c)
IarcCSmid.int(7,5,int,t,c=.4)

IarcCSmid.int(1,3,int,t,c)

IarcCSmid.int(9,11,int,t,c)

IarcCSmid.int(19,1,int,t,c)
IarcCSmid.int(19,19,int,t,c)

IarcCSmid.int(3,5,int,t,c)

#or try
Rv<-rel.vert.mid.int(3,int,c)$rv
IarcCSmid.int(3,5,int,t,c,rv=Rv)

IarcCSmid.int(7,5,int,t,c)