# Number of Arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle interval case 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 (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:revstat-2016;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r 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 $M_c=a+c(b-a)$. ## Returns 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. ## Examples ```r 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) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `num.arcsCSend.int`, `num.arcsPEmid.int`, and `num.arcsPEend.int` ## Author(s) Elvan Ceyhan

num.arcsCSmid.int function