Dear All,
For some time now, I've been fiddling around with a couple algorithms to
estimate the parameters of a mixture of normal distributions, presented as
a frequency distribution.
After trying several algorithms, I decided to use nonlinear minimisation
using as objective function the log-likelihood of a mixture of normal
distributions.
However, I found out that in many cases these tended to underestimate the
means of the last sub-populations. I think this may be related to the fact
that sometimes the distribution may be somewhat truncated, i.e. we do not
get the smallest and largest individuals.
I believe a solution might be to use a likelihood function that
incorporates the possibility of truncation of the distribution. Until now,
however, I did not manage to get hold of a good description of how to do
it, so I would like to ask if anyone can tell what the appropriate
likelihood function would be, and preferably some easy-to-find reference on
it.
Any help would be highly appreciated.
Thanks,
Pedro
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