pcds (version 0.1.4)

NumArcsPEend1D: Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case

Description

Returns the number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) whose vertices are a 1D numerical data set, dat, outside the interval int\(=(a,b)\).

PE proximity region is constructed only with expansion parameter \(r \ge 1\) for points outside the interval \((a,b)\). End vertex regions are based on the end points of the interval, i.e., the corresponding vertex region is an interval as \((-\infty,a)\) or \((b,\infty)\) for the interval \((a,b)\). For the number of arcs, loops are not allowed, so arcs are only possible for points outside the interval, int, for this function.

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

Usage

NumArcsPEend1D(dat, r, int)

Value

Number of arcs for the PE-PCD with vertices being 1D data set, dat, expansion parameter, \(r \ge 1\), for the end intervals.

Arguments

dat

A vector of 1D points which constitute the vertices of the digraph.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

int

A vector of two real numbers representing an interval.

Author

Elvan Ceyhan

References

See Also

NumArcsPEmid1D, NumArcsCSmid1D, and NumArcsCSend1D

Examples

a<-0; b<-10; int<-c(a,b)

n<-5
datL<-runif(n,a-5,a)
datR<-runif(n,b,b+5)
dat<-c(datL,datR)

r<-2
NumArcsPEend1D(dat,r,int)

NumArcsPEend1D(dat,r=1.2,int)
NumArcsPEend1D(dat,r=4,int)

n<-10  #try also n<-20
dat2<-runif(n,a-5,b+5)
NumArcsPEend1D(dat2,r,int)

NumArcsPEend1D(dat,r,int)