IarcPEmid.int {pcds}R Documentation

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

Description

Returns I(p2NPE(p1,r,c))I(p_2 \in N_{PE}(p_1,r,c)) for points p1p_1 and p2p_2, that is, returns 1 if p2p_2 is in NPE(p1,r,c)N_{PE}(p_1,r,c), returns 0 otherwise, where NPE(x,r,c)N_{PE}(x,r,c) is the PE proximity region for point xx and is constructed with expansion parameter r1r \ge 1 and centrality parameter c(0,1)c \in (0,1) for the interval (a,b)(a,b).

PE 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(0,1)c \in (0,1). For the interval, int=(a,b)=(a,b), the parameterized center is Mc=a+c(ba)M_c=a+c(b-a). rv is the index of the vertex region p1p_1 resides, with default=NULL. If p1p_1 and p2p_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 (2012, 2016)).

Usage

IarcPEmid.int(p1, x2, int, r, c = 0.5, rv = NULL)

Arguments

p1, x2

1D points; p1p_1 is the point for which the proximity region, NPE(p1,r,c)N_{PE}(p_1,r,c) is constructed and p2p_2 is the point which the function is checking whether its inside NPE(p1,r,c)N_{PE}(p_1,r,c) 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 1\ge 1.

c

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

rv

The index of the vertex region p1p_1 resides, with default=NULL.

Value

I(p2NPE(p1,r,c))I(p_2 \in N_{PE}(p_1,r,c)) for points p1p_1 and p2p_2 that is, returns 1 if p2p_2 is in NPE(p1,r,c)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.

Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.

See Also

IarcPEend.int, IarcCSmid.int, and IarcCSend.int

Examples

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

IarcPEmid.int(7,5,int,r,c)
IarcPEmid.int(1,3,int,r,c)


[Package pcds version 0.1.8 Index]