funsMuVarPE1D: Returns the mean and (asymptotic) variance of arc density of...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

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 (\insertCiteceyhan:metrika-2012;textualpcds).

Usage

mu1PE1D(r, c)

muPE1D(r, c)

fvar1(r, c)

fvar2(r, c)

asyvarPE1D(r, c)

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).

Value

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

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

muCS1D and asyvarCS1D

Examples

## Not run: 
#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")

## End(Not run)

## Not run: 
#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")

## End(Not run)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.