NCSint {pcds}

The end points of the Central Similarity (CS) Proximity Region for a point - one interval case

Description

Returns the end points of the interval which constitutes the CS proximity region for a point in the interval int=(a,b)=(rv=1,rv=2).

CS proximity region is constructed with respect to the interval int with expansion parameter t>0 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 CS proximity region is constructed whether x is inside or outside the interval int.

See also (Ceyhan (2016)).

Usage

NCSint(x, int, t, c = 0.5)

Arguments

x

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

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

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

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

NPEint and NCStri

Examples

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

NCSint(7,int,t,c)
NCSint(17,int,t,c)
NCSint(1,int,t,c)
NCSint(-1,int,t,c)

NCSint(3,int,t,c)
NCSint(4,int,t,c)
NCSint(a,int,t,c)