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And where defined,
it is probably the better default for fit to redispatch to than fit_mle.
It also might be worth considering fit to take an argument as to if to fit for an unbiased esimator or to fit as a maximum likelyhood estimator.
sounds ok to replace fit_mle with an unbiased estimation when available, people who want MLE will call it specifically
You can't really have an "unbiased distribution estimator", all you can really say is that certain functions of the estimated distribution (such as the first and second moments) are unbiased.
That, and being unbiased is only important in particular situations, e.g. in pseudo-marginal Metropolis–Hastings algorithm, otherwise you'd willingly trade bias and variance.