pcds (version 0.1.8)

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 asy.varPE1D and their auxiliary functions.

muPE1D returns the mean of the (arc) density of PE-PCD and asy.varPE1D 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 \(r \ge 1\).

asy.varPE1D 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)
asy.varPE1D(r, c)

Value

muPE1D returns the mean and asy.varPE1D 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 asy.varCS1D

Examples

# \donttest{
#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")
# }

# \donttest{
#Examples for asy.varPE1D
asy.varPE1D(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]<-asy.varPE1D(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")
# }