pcds (version 0.1.6)

NumArcsCSmid.int: Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case

Description

Returns the number of arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) whose vertices are the given 1D numerical data set, Xp.

CS proximity region \(N_{CS}(x,t,c)\) is defined with respect to the interval int\(=(a,b)\) for this function. CS proximity region is constructed with expansion parameter \(t>0\) and centrality parameter \(c \in (0,1)\).

Vertex regions are based on the center associated with the centrality parameter \(c \in (0,1)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\) and for the number of arcs, loops are not allowed so arcs are only possible for points inside the middle interval int for this function.

See also (ceyhan:revstat-2016;textualpcds).

Usage

NumArcsCSmid.int(Xp, int, t, c = 0.5)

Value

Number of arcs for the PE-PCD whose vertices are the 1D data set, Xp, with expansion parameter, \(r \ge 1\), and centrality parameter, \(c \in (0,1)\). PE proximity regions are defined only for Xp points inside the interval int, i.e., arcs are possible for such points only.

Arguments

Xp

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

int

A vector of two real numbers representing an interval.

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\(=(a,b)\) 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

NumArcsCSend.int, NumArcsPEmid.int, and NumArcsPEend.int

Examples

if (FALSE) {
c<-.4
t<-2
a<-0; b<-10; int<-c(a,b)

n<-10
Xp<-runif(n,a,b)
NumArcsCSmid.int(Xp,int,t,c)
NumArcsCSmid.int(Xp,int,t,c=.3)
NumArcsCSmid.int(Xp,int,t=1.5,c)
}