pcds (version 0.1.4)

funsMuVarCS1D: 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 asyvarCS1D.

muCS1D returns the mean of the (arc) density of CS-PCD and asyvarCS1D 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:revstat-2016;textualpcds).

Usage

muCS1D(t, c)
asyvarCS1D(t, c)

Value

muCS1D returns the mean and asyvarCS1D returns the asymptotic variance of the arc density of CS-PCD for uniform data in an interval

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 $M_c=a+c(b-a)$.

Author

Elvan Ceyhan

References

See Also

muPE1D and asyvarPE1D

Examples

# \donttest{
#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")
# }

# \donttest{
#Examples for asyvarCS1D
asyvarCS1D(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]<-asyvarCS1D(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")
# }