funsMuVarCS1D {pcds}

Returning the mean and (asymptotic) variance of arc density of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle interval case

Description

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 (Ceyhan (2016)).

Usage

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).

Value

muCS1D returns the mean and asy.varCS1D returns the asymptotic variance of the arc density of CS-PCD for uniform data in an interval

Author(s)

Elvan Ceyhan

References

Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.

See Also

muPE1D and asy.varPE1D

Examples

#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")