unfoldr (version 0.2)

em.saltykov: Expectation Maximization algorithm

Description

Estimation of empirical sphere diameter distribution

Usage

em.saltykov(y, bin, maxIt = 32)

Arguments

y

vector of observed absolute frequencies of circle diameters

bin

non-decreasing vector of class limits

maxIt

maximum number of iterations used

Value

• vector of count data of absolute frequenties of sphere diameters

Details

The function performs the EM algorithm.

References

Ohser, J. and Muecklich, F. Statistical analysis of microstructures in materials science J. Wiley & Sons, 2000

Examples

## beta distributed radii
lam <-3000
theta <- list("lam"=lam,"radii"=list("shape1"=2,"shape2"=4))
S <- simSphereSystem(theta,rdist="rbeta", box=list(c(0,5)),pl=101)

sp <- planarSection(S,d=2.5)
ret <- unfold(sp,nclass=20)
 
## Point process intensity
cat("Intensities: ", sum(ret$N_V)/25, "vs.",lam,"\n")
 
## original diameters
r3d <- unlist(lapply(S,function(x) 2.0*x$r))
rest3d <- unlist(lapply(2:(length(ret$breaks)),
            function(i) rep(ret$breaks[i],sum(ret$N_V[i-1]))))
 
op <- par(mfrow = c(1, 2))
hist(r3d[r3d<=max(ret$breaks)], breaks=ret$breaks, main="Radius 3d",
     freq=FALSE, col="gray",xlab="r")
hist(rest3d, breaks=ret$breaks,main="Radius estimated",
     freq=FALSE, col="gray", xlab="r")
par(op)