1d:T77e,# Returns the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - end-interval case Two functions: `muCSend.int` and `asy.varCSend.int`. `muCSend.int` returns the mean of the arc density of CS-PCD and `asy.varCSend.int` returns the asymptotic variance of the arc density of CS-PCD for a given expansion parameter $t>0$ for 1D uniform data in the left and right end-intervals for the interval $(a,b)$. 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 muCSend.int(t) asy.varCSend.int(t) ``` ## Arguments - `t`: A positive real number which serves as the expansion parameter in CS proximity region. ## Returns `muCSend.int` returns the mean and `asy.varCSend.int` returns the asymptotic variance of the arc density of CS-PCD for uniform data in end-intervals ## Details funsMuVarCSend.int ## Examples ```r #Examples for muCSend.int muCSend.int(1.2) tseq<-seq(0.01,5,by=.05) ltseq<-length(tseq) mu.end<-vector() for (i in 1:ltseq) { mu.end<-c(mu.end,muCSend.int(tseq[i])) } oldpar <- par(no.readonly = TRUE) par(mar = c(5,4,4,2) + 0.1) plot(tseq, mu.end,type="l", ylab=expression(paste(mu,"(t)")),xlab="t",lty=1,xlim=range(tseq),ylim=c(0,1)) par(oldpar) #Examples for asy.varCSend.int asy.varCSend.int(1.2) tseq<-seq(.01,5,by=.05) ltseq<-length(tseq) var.end<-vector() for (i in 1:ltseq) { var.end<-c(var.end,asy.varCSend.int(tseq[i])) } oldpar <- par(no.readonly = TRUE) par(mar=c(5,5,4,2)) plot(tseq, var.end,type="l",xlab="t",ylab=expression(paste(sigma^2,"(t)")),lty=1,xlim=range(tseq)) par(oldpar) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `muPEend.int` and `asy.varPEend.int` ## Author(s) Elvan Ceyhan

funsMuVarCSend.int function