num.arcsCSmid.int {pcds}

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 (2016)).

Usage

num.arcsCSmid.int(Xp, int, t, c = 0.5)

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).

Value

Number of arcs for the CS-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.

Author(s)

Elvan Ceyhan

References

Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.

See Also

num.arcsCSend.int, num.arcsPEmid.int, and num.arcsPEend.int

Examples

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

n<-10
Xp<-runif(n,a,b)
num.arcsCSmid.int(Xp,int,t,c)

num.arcsCSmid.int(Xp,int,t,c=.3)

num.arcsCSmid.int(Xp,int,t=1.5,c)

#num.arcsCSmid.int(Xp,int,t,c+5) #gives error
#num.arcsCSmid.int(Xp,int,t,c+10)

n<-10  #try also n<-20
Xp<-runif(n,a-5,b+5)
num.arcsCSint(Xp,int,t,c)

Xp<-runif(n,a+10,b+10)
num.arcsCSmid.int(Xp,int,t,c)

n<-10
Xp<-runif(n,a,b)
num.arcsCSmid.int(Xp,int,t,c)