# The arcs of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - end-interval case An object of class `"PCDs"`. Returns arcs of PE-PCD as tails (or sources) and heads (or arrow ends) and related parameters and the quantities of the digraph. The vertices of the PE-PCD are the 1D data points in `Xp` in the end-interval case. `Yp` determines the end points of the end-intervals. For this function, PE proximity regions are constructed data points outside the intervals based on `Yp` points with expansion parameter $r \ge 1$. That is, for this function, arcs may exist for points only inside end-intervals. It also provides various descriptions and quantities about the arcs of the PE-PCD such as number of arcs, arc density, etc. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:metrika-2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r arcsPEend.int(Xp, Yp, r) ``` ## Arguments - `Xp`: A set or `vector` of 1D points which constitute the vertices of the PE-PCD. - `Yp`: A set or `vector` of 1D points which constitute the end points of the intervals. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$. ## Returns A `list` with the elements - **type**: A description of the type of the digraph - **parameters**: Parameters of the digraph, here, it is the expansion parameter. - **tess.points**: Tessellation points, i.e., points on which the tessellation of the study region is performed, here, tessellation is the intervalization based on `Yp`. - **tess.name**: Name of the tessellation points `tess.points` - **vertices**: Vertices of the digraph, `Xp` points - **vert.name**: Name of the data set which constitutes the vertices of the digraph - **S**: Tails (or sources) of the arcs of PE-PCD for 1D data in the end-intervals - **E**: Heads (or arrow ends) of the arcs of PE-PCD for 1D data in the end-intervals - **mtitle**: Text for `"main"` title in the plot of the digraph - **quant**: Various quantities for the digraph: number of vertices, number of partition points, number of intervals (which is 2 for end-intervals), number of arcs, and arc density. ## Examples ```r r<-2 a<-0; b<-10; int<-c(a,b); #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-15; ny<-4; #try also nx<-40; ny<-10 or nx<-1000; ny<-10; set.seed(1) xf<-(int[2]-int[1])*.5 Xp<-runif(nx,a-xf,b+xf) Yp<-runif(ny,a,b) #try also Yp<-runif(ny,a,b)+c(-10,10) Arcs<-arcsPEend.int(Xp,Yp,r) Arcs summary(Arcs) plot(Arcs) S<-Arcs$S E<-Arcs$E jit<-.1 yjit<-runif(nx,-jit,jit) Xlim<-range(a,b,Xp,Yp) xd<-Xlim[2]-Xlim[1] plot(cbind(a,0),pch=".", main="arcs of PE-PCDs for points (jittered along y-axis)\n in end-intervals ", xlab=" ", ylab=" ", xlim=Xlim+xd*c(-.05,.05),ylim=3*c(-jit,jit)) abline(h=0,lty=1) points(Xp, yjit,pch=".",cex=3) abline(v=Yp,lty=2) arrows(S, yjit, E, yjit, length = .05, col= 4) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `arcsPEmid.int`, `arcsPE1D` , `arcsCSmid.int`, `arcsCSend.int` and `arcsCS1D` ## Author(s) Elvan Ceyhan

arcsPEend.int function