pcds (version 0.1.6)

NumArcsPEint: Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one interval case

Description

Returns the number of arcs and various other quantities, vectors, and lists for Proportional Edge Proximity Catch Digraph (PE-PCD) whose vertices are the data points in Xp in the one middle interval case.

The data points could be inside or outside the interval is int\(=(a,b)\). PE proximity region is constructed with an expansion parameter \(r \ge 1\) and a centrality parameter \(c \in (0,1)\). int determines the end points of the interval.

The PE proximity region is constructed for both points inside and outside the interval, hence the arcs may exist for all points inside or outside the interval.

See also (ceyhan:metrika-2012;textualpcds).

Usage

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

Value

A list with the elements

num.arcs

Total number of arcs in all intervals (including the end intervals), i.e., the number of arcs for the entire PE-PCD

num.in.range

Number of Xp points in the interval int

num.in.ints

The vector of number of Xp points in the partition intervals (including the end intervals)

int.num.arcs

The vector of the number of arcs of the components of the PE-PCD in the partition intervals (including the end intervals)

data.int.ind

A vector of indices of partition intervals in which data points reside. Partition intervals are numbered from left to right with 1 being the left end interval.

Arguments

Xp

A set of 1D points which constitute the vertices of PE-PCD.

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 \(M_c=a+c(b-a)\).

Author

Elvan Ceyhan

References

See Also

NumArcsPEmid.int, NumArcsPEend.int, and NumArcsCSint

Examples

if (FALSE) {
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)
NumArcsPEint(Xp,int,r,c)
NumArcsPEint(Xp,int,r,c=.3)
NumArcsPEint(Xp,int,r=1.5,c)
}