pcds (version 0.1.4)

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

Description

Returns the number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) whose vertices are the 1D data set dat in the one-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 \(c \in (0,1)\).

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(dat, r, c = 0.5, int)

Value

Number of arcs for the PE-PCD whose vertices are the 1D data set, dat, with expansion parameter, \(r \ge 1\), and centrality parameter, \(c \in (0,1)\).

Arguments

dat

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

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\(=(a,b)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\); default=0.5

int

A vector of two real numbers representing an interval.

Author

Elvan Ceyhan

References

See Also

NumArcsPEmid1D, NumArcsPEend1D, and NumArcsCSint

Examples

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

n<-10
dat<-runif(n,a,b)
NumArcsPEint(dat,r,c,int)

NumArcsPEint(3,r,c,int)

NumArcsPEint(dat,r,c=.3,int)

NumArcsPEint(dat,r=1.5,c,int)

n<-10  #try also n<-20
dat<-runif(n,a,b)

NumArcsPEint(dat,r,c,int)

dat<-runif(n,a+10,b+10)
NumArcsPEint(dat,r,c,int)

n<-10
dat<-runif(n,a,b)
NumArcsPEint(dat,r,c,int)