# Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case Two functions: `muCS1D` and `asy.varCS1D`. `muCS1D` returns the mean of the (arc) density of CS-PCD and `asy.varCS1D` returns the (asymptotic) variance of the arc density of CS-PCD for a given centrality parameter $c \in (0,1)$ and an expansion parameter $t>0$ and 1D uniform data in a finite interval $(a,b)$, i.e., data from $U(a,b)$ distribution. 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 muCS1D(t, c) asy.varCS1D(t, c) ``` ## Arguments - `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 $M_c=a+c(b-a)$. ## Returns `muCS1D` returns the mean and `asy.varCS1D` returns the asymptotic variance of the arc density of CS-PCD for uniform data in an interval ## Examples ```r #Examples for muCS1D muCS1D(1.2,.4) muCS1D(1.2,.6) tseq<-seq(0.01,5,by=.05) cseq<-seq(0.01,.99,by=.05) ltseq<-length(tseq) lcseq<-length(cseq) mu.grid<-matrix(0,nrow=ltseq,ncol=lcseq) for (i in 1:ltseq) for (j in 1:lcseq) { mu.grid[i,j]<-muCS1D(tseq[i],cseq[j]) } persp(tseq,cseq,mu.grid, xlab="t", ylab="c", zlab="mu(t,c)",theta = -30, phi = 30, expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed") #Examples for asy.varCS1D asy.varCS1D(1.2,.8) tseq<-seq(0.01,5,by=.05) cseq<-seq(0.01,.99,by=.05) ltseq<-length(tseq) lcseq<-length(cseq) var.grid<-matrix(0,nrow=ltseq,ncol=lcseq) for (i in 1:ltseq) for (j in 1:lcseq) { var.grid[i,j]<-asy.varCS1D(tseq[i],cseq[j]) } persp(tseq,cseq,var.grid, xlab="t", ylab="c", zlab="var(t,c)", theta = -30, phi = 30, expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed") ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `muPE1D` and `asy.varPE1D` ## Author(s) Elvan Ceyhan

funsMuVarCS1D function