inci.matPE1D {pcds}

Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple 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 Yp determines the end points of the intervals (in the multi-interval case). If there are duplicates of Yp points, only one point is retained for each duplicate value, and a warning message is printed. 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.matPE1D(Xp, Yp, r, c = 0.5)

Arguments

Xp

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

Yp

a set of 1D points which constitutes the end points of the intervals that partition the real line.

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, (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 Yp determines the end points of the intervals (in the multi-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.matCS1D, inci.matPEtri, and inci.matPE

Examples

r<-2
c<-.4
a<-0; b<-10;
nx<-10; ny<-4

set.seed(1)
Xp<-runif(nx,a,b)
Yp<-runif(ny,a,b)

IM<-inci.matPE1D(Xp,Yp,r,c)
IM

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