ArcsPEint: The arcs of Proportional Edge Proximity Catch Digraph...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - one interval case

Description

An object of class "PCDs". Returns arcs as tails (or sources) and heads (or arrow ends) for 1D data set Xp as the vertices of PE-PCD. int determines the end points of the interval.

For this function, PE proximity regions are constructed data points inside or outside the interval based on int points with expansion parameter r \ge 1 and centrality parameter c \in (0,1). That is, for this function, arcs may exist for points in the middle or end intervals. It also provides various descriptions and quantities about the arcs of the PE-PCD such as number of arcs, arc density, etc.

See also (\insertCiteceyhan:metrika-2012;textualpcds).

Usage

arcsPEint(Xp, int, r, c = 0.5)

Arguments

Xp	A set or vector of 1D points which constitute the vertices of the PE-PCD.
int	A vector of two 1D points which constitutes the end points of the 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

A list with the elements

type	A description of the type of the digraph
parameters	Parameters of the digraph, here, they are expansion and centrality parameters.
tess.points	Points on which the tessellation of the study region is performed, here, tessellation is the intervalization of the real line based on int points.
tess.name	Name of data set used in tessellation, it is int for this function
vertices	Vertices of the digraph, Xp points
vert.name	Name of the data set which constitute the vertices of the digraph
S	Tails (or sources) of the arcs of PE-PCD for 1D data
E	Heads (or arrow ends) of the arcs of PE-PCD for 1D data
mtitle	Text for "main" title in the plot of the digraph
quant	Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

arcsPE1D, arcsPEmid.int, arcsPEend.int, and arcsCS1D

Examples

## Not run: 
r<-2
c<-.4
a<-0; b<-10; int<-c(a,b);

#n is number of X points
n<-10; #try also n<-20

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

set.seed(1)
Xp<-runif(n,a-xf,b+xf)

Arcs<-arcsPEint(Xp,int,r,c)
Arcs
summary(Arcs)
plot(Arcs)

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.