On Wed, Mar 11, 2015 at 5:15 PM, <josef.pktd@gmail.com> wrote:

RLM produces an unbiased estimator of the mean or mean function for symmetric distribution and is calibrated for the normal distribution. I don't know how well this is approximated by the log of an exponentially distributed variable, but it won't exactly satisfy the assumptions.

Yes, RLM will heavily weight the tail that before the transform is almost 0 and after becomes arbitrary large negative values.

There should be a more direct way of estimating the parameter for the exponential distribution in a robust way, but I never tried.
(one idea would be to estimate a trimmed mean and use the estimated distribution to correct for the trimming. scipy.stats.distributions have an `expect` method that can be used to calculate the mean of a trimmed distribution, i.e. conditional on lower and upper bounds)

Thanks, I wasn't aware of the expect method. However I already tried to trim the distribution (on the left-side). But the thresholds are arbitrary and I would like to make the fitting not dependent on them.

What's your sample size?
(for very large sample sizes one approach that is sometimes used, is to fit a distribution to the central part of a histogram)

The sample size is from a few 100s to a few 1000s, not really huge. The problem is that I don't know if there is a "robust" a criterion to trim the distribution, and then what would be the accuracy of such a fit.

Antonio