Nothing

```
# Calcualtion of the vl, l=1,...,L-1 as a function of pl, l=1, ..., L
vofp.cgb2 <- function(pl){
ncomp <- length(pl)
vl <- rep(0, ncomp-1)
pL <- pl[ncomp]
vl <- log(pl[-ncomp]/pL)
return(vl)
}
# Calculation of the pl, l=1,...,L as a function of vl, l=1, ..., L-1
pofv.cgb2 <- function(vl){
pl <- exp(vl)/(1+sum(exp(vl)))
pL <- 1/(1+sum(exp(vl)))
pl <- c(pl,pL)
return(pl)
}
# Log-likelihood function
logl.cgb2 <- function(fac, pl, w=rep(1, dim(fac)[1])){
sw <- sum(w)
mixt <- fac%*%pl
logcomp <- log(mixt)
logL <- sum(w*logcomp)/sw
return(logL)
}
# Score functions
# Weighted mean of the scores
scores.cgb2 <- function(fac, pl, w=rep(1, dim(fac)[1])){
sw <- sum(w)
L <-length(pl)
denom <- fac%*%pl
num <- fac[,-L]
midt <- num/as.vector(denom) - 1
if (L>2) dlogL <- pl[-L]*colSums(midt*w)
if (L==2) dlogL <- pl[-L]*sum(midt*w)
return(dlogL/sw)
}
# Maximum pseudo-likelihood estimation, GB2 as a compound distribution
ml.cgb2 <- function (fac, pl0, w = rep(1, dim(fac)[1]), maxiter = 100, fnscale=length(w))
{
vl0 <- vofp.cgb2(pl0)
fn <- function(vl, fac, w) {
pl <- pofv.cgb2(vl)
return(-logl.cgb2(fac, pl, w))
}
gr <- function(vl, fac, w) {
pl <- pofv.cgb2(vl)
return(-scores.cgb2(fac, pl, w))
}
opt <- optim(vl0, fn, gr, fac, w, method = "BFGS", control = list(maxit = maxiter,
fnscale = fnscale), hessian = FALSE)
vlf <- opt$par
plf <- pofv.cgb2(vlf)
return(list(plf, opt))
}
```

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