NPEint {pcds}

The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case

Description

Returns the end points of the interval which constitutes the PE proximity region for a point in the interval int=(a,b)=(rv=1,rv=2). PE proximity region is constructed with respect to the interval int with expansion parameter r \ge 1 and centrality parameter c \in (0,1).

Vertex regions are based on the (parameterized) center, M_c, which is M_c=a+c(b-a) for the interval, int=(a,b). The PE proximity region is constructed whether x is inside or outside the interval int.

See also (Ceyhan (2012)).

Usage

NPEint(x, int, r, c = 0.5)

Arguments

x

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

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 \ge 1.

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

The interval which constitutes the PE proximity region for the point x

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.

See Also

NCSint, NPEtri and NPEtetra

Examples

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

NPEint(7,int,r,c)
NPEint(17,int,r,c)
NPEint(1,int,r,c)
NPEint(-1,int,r,c)