inci.matPEint {pcds}

Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - one interval case

Description

Returns the incidence matrix for the PE-PCD for a given 1D numerical data set, Xp, as the vertices of the digraph and int determines the end points of the interval (in the one interval case). Loops are allowed, so the diagonal entries are all equal to 1.

PE proximity region is constructed with an expansion parameter r \ge 1 and a centrality parameter c \in (0,1).

See also (Ceyhan (2012)).

Usage

inci.matPEint(Xp, int, r, c = 0.5)

Arguments

Xp

a set of 1D points which constitutes the vertices of the digraph.

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 middle intervals with the default c=.5. For the interval, int=(a,b), the parameterized center is M_c=a+c(b-a).

Value

Incidence matrix for the PE-PCD with vertices being 1D data set, Xp, and int determines the end points of the intervals (in the one interval case)

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

inci.matCSint, inci.matPE1D, inci.matPEtri, and inci.matPE

Examples

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

xf<-(int[2]-int[1])*.1

set.seed(123)

n<-10
Xp<-runif(n,a-xf,b+xf)

IM<-inci.matPEint(Xp,int,r,c)
IM

dom.num.greedy(IM)
Idom.num.up.bnd(IM,6)
dom.num.exact(IM)

inci.matPEint(Xp,int+10,r,c)