You are right, the initial parameter estimates sometimes need to be really good – especially in the maximum likelihood models I have been trying in the bbmle package.

You mean look at the derivative of the function to obtain parameter estimates? I think this is kind of what the Bhattacharya approach to parameter estimation does (not on the density function but on sampling data) – except it looks in log space. It does a really good job but does require some human oversight. It’s discussed in this paper. The approach is still used by some labs to help the define normal ranges from all blood collections under the assumption that the sick and well populations form two Gaussian modes (almost never true).

Anyway – I am going to look at the derivatives as you suggest.

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