pcds (version 0.1.2)

IndNPEint: 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 \(I(x_2 \in N_{PE}(x_1,r,c))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{PE}(x_1,r,c)\), 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 \(x_1\) and \(x_2\) 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 \(x_1\) and \(x_2\) are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph).

See also (ceyhan:metrika-2012;textualpcds).

Usage

IndNPEint(x1, x2, r, c = 0.5, int)

Arguments

x1

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

x2

A 1D point for which it is checked whether it resides in the proximity region of \(x_1\) or not.

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\(=(a,b)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\), and default=0.5

int

A vector of two real numbers representing an interval.

Value

\(I(x_2 \in N_{PE}(x_1,r,c))\) for x2, that is, returns 1 if \(x_2\) in \(N_{PE}(x_1,r,c)\), returns 0 otherwise

References

See Also

IndNPEmid1D, IndNPEend1D and IndNCSint

Examples

# NOT RUN {
c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)

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

IndNPEint(-17,17,r,c,int)

IndNPEint(3,5,r,c,int)
IndNPEint(3,3,r,c,int)
IndNPEint(4,5,r,c,int)
IndNPEint(a,5,r,c,int)

c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)
IndNPEint(7,5,r,c,int)

# }