Fitting distributions is a little bit different than the usual model fitting scenario where least squares is appropriate. Sometimes people do things like construct a histogram and then do a least squares fit to the bin heights, but that procedure doesn't satisfy the usual assumptions that justify least squares (observations with independent, equal variance, Gaussian errors).

Cosma Shalizi has written some interesting posts on this subject, and also published papers in statistics journals:

http://bactra.org/weblog/491.html