Sorry for bumping this old thread, but @Tamas_Papp seems knowledgeable and the topic is very close to what I want to achieve:
I have a random variable X which I can e.g. sample. I know that there is a normalizing transformation for X, namely (µ - X)^t is known to be normally distributed for some (µ, t).
What is the best/simplest/the most precise way of estimating µ and t?
(sampling of X=Xₖ is relatively cheap, of the cost ~ randn(k)).
What I was thinking about is MC → quantile estimation → fitting the appropriate normcdf and deciding (µ,t) based on mse of this approximation, but maybe something better is at hand?