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Regarding fitting a Weibull two parameters probability density function (pdf), with the fitdistr from MASS package, in R:

1 - What is the iteration algorithm/method used for scale and shape Maximum Likelihood Estimation (MLE)?

I used to think it was Newton-Raphson, but after looking here and here I got confused.

There are Nelder–Mead, quasi-Newton and conjugate-gradient algorithms, but I am not sure which one is used for the iteration process on Weibull 2 parameters pdf MLE.

2 - Based on the answer to question 1, what would be a good reference to study the method?

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  1. It's BFGS

  2. I'm not too sure, but the basic idea is to do Newton's method, but use an approximation to the inverse of the Hessian instead of the true inverse of the Hessian. There is a good explanation in these notes (pdf) but I am not sure that it is enough to do an implementation. However, there do seem to be a lot of references on BFGS. It even has a Facebook page.

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