[R] MLE for bimodal distribution

[_nico_]

Hello everyone,

I'm trying to use mle from package stats4 to fit a bi/multi-modal
distribution to some data, but I have some problems with it.
Here's what I'm doing (for a bimodal distribution):

# Build some fake binormally distributed data, the procedure fails also with
real data, so the problem isn't here
data = c(rnorm(1000, 3, 0.5), rnorm(500, 5, 0.3))
# Just to check it's bimodal
plot(density(data))
f = function(m, s, m2, s2, w)
{
-log( sum(w*dnorm(data, mean=m, sd=s)) + sum((1-w)*dnorm(data, mean=m2,
sd=s2)) )
}

res = mle(f, start=list("m"=3, "s"=0.5, "m2"=5, "s2"=0.35, "w"=0.6))

This gives an error:
Error in optim(start, f, method = method, hessian = TRUE, ...) : 
  non-finite finite-difference value [2]
In addition: There were 50 or more warnings (use warnings() to see the first
50)
And the warnings are about dnorm producing NaNs

So, my questions are:
1) What does "non-finite finite-difference value" mean? My guess would be
that an Inf was passed somewhere where a finite number was expected...? I'm
not sure how optim works though...
2) Is the log likelihood function I wrote correct? Can I use the same type
of function for 3 modes?
3) What should I do to avoid function failure? I tried by changing the
parameters, but it did not work.
4) Can I put constraints to the parameters? In particular, I would like w to
be between 0 and 1.
5) Is there a way to get the log-likelihood value, so that I can compare
different extimations?
6) Do you have any (possibly a bit "pratically oriented") readings about MLE
to suggest?

Thanks in advance
Nico
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