pcds (version 0.1.6)

funsMuVarPE1D: Returns the mean and (asymptotic) variance of arc density of Proportional Edge Proximity Catch Digraph (PE-PCD) for 1D data - middle interval case

Description

The functions muPE1D and asyvarPE1D and their auxiliary functions.

muPE1D returns the mean of the (arc) density of PE-PCD and asyvarPE1D returns the (asymptotic) variance of the arc density of PE-PCD for a given centrality parameter $c\in (0,1)$ and an expansion parameter $r\ge 1$ and for 1D uniform data in a finite interval $(a,b)$, i.e., data from $U(a,b)$ distribution.

muPE1D uses auxiliary (internal) function mu1PE1D which yields mean (i.e., expected value) of the arc density of PE-PCD for a given $c\in (0,1/2)$ and $r\ge 1$.

asyvarPE1D uses auxiliary (internal) functions fvar1 which yields asymptotic variance of the arc density of PE-PCD for $c\in (1/4,1/2)$ and $r\ge 1$; and fvar2 which yields asymptotic variance of the arc density of PE-PCD for $c\in (0,1/4)$ and $r\ge 1$.

See also (ceyhan:metrika-2012;textualpcds).

Usage

mu1PE1D(r, c)
muPE1D(r, c)
fvar1(r, c)
fvar2(r, c)
asyvarPE1D(r, c)

Value

muPE1D returns the mean and asyvarPE1D returns the asymptotic variance of the arc density of PE-PCD for $U(a,b)$ data

Arguments

r

A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$.

c

A positive real number in $(0,1)$ parameterizing the center inside int$=(a,b)$. For the interval, $(a,b)$, the parameterized center is $M_c=a+c(b-a)$.

Author

Elvan Ceyhan

References

See Also

muCS1D and asyvarCS1D

Examples

if (FALSE) {
#Examples for muPE1D
muPE1D(1.2,.4)
muPE1D(1.2,.6)

rseq<-seq(1.01,5,by=.1)
cseq<-seq(0.01,.99,by=.1)

lrseq<-length(rseq)
lcseq<-length(cseq)

mu.grid<-matrix(0,nrow=lrseq,ncol=lcseq)
for (i in 1:lrseq)
  for (j in 1:lcseq)
  {
    mu.grid[i,j]<-muPE1D(rseq[i],cseq[j])
  }

persp(rseq,cseq,mu.grid, xlab="r", ylab="c", zlab="mu(r,c)", theta = -30, phi = 30,
expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed")
}

if (FALSE) {
#Examples for asyvarPE1D
asyvarPE1D(1.2,.8)

rseq<-seq(1.01,5,by=.1)
cseq<-seq(0.01,.99,by=.1)

lrseq<-length(rseq)
lcseq<-length(cseq)

var.grid<-matrix(0,nrow=lrseq,ncol=lcseq)
for (i in 1:lrseq)
  for (j in 1:lcseq)
  {
    var.grid[i,j]<-asyvarPE1D(rseq[i],cseq[j])
  }

persp(rseq,cseq,var.grid, xlab="r", ylab="c", zlab="var(r,c)", theta = -30, phi = 30,
expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.05, ticktype = "detailed")
}