pcds (version 0.1.1)

NumArcsCSint: Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one interval case

Description

Returns the number of arcs of Central Similarity Proximity Catch Digraphs (CS-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 $int=(a,b)$.

CS proximity region is constructed with an expansion parameter $t>0$ and a centrality parameter c in $(0,1)$. CS 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:revstat-2016;textualpcds).

Usage

NumArcsCSint(dat, t, c = 0.5, int)

Arguments

dat

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

t

A positive real number which serves as the expansion parameter in CS proximity region.

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.

Value

Number of arcs for the CS-PCD whose vertices are the 1D data set, dat, with expansion parameter, $t>0$, and centrality parameter, c in $(0,1)$.

References

See Also

NumArcsCSmid1D, NumArcsCSend1D, and NumArcsPEint

Examples

# NOT RUN {
c<-.4
t<-2
a<-0; b<-10; int<-c(a,b)

n<-10
dat<-runif(n,a,b)
NumArcsCSint(dat,t,c,int)

NumArcsCSint(3,t,c,int)

NumArcsCSint(dat,t,c=.3,int)

NumArcsCSint(dat,t=1.5,c,int)

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

NumArcsCSint(dat,t,c,int)

n<-10
dat<-runif(n,a,b)
NumArcsCSint(dat,t,c,int)

# }