[R] Distribution Fitting

[Lorenzo Isella]

Hi,
I know this is a bit off-topic, but I am quite puzzled. I am going
through several papers about aerosol physics and in this field you
often have determine the parameters of a distribution to match your
experimental data (one typically uses a Gaussian mixture).
However, in many cases people plot a normalized empirical distribution
function and then perform some least-square fitting rather than using
likelihood functions.
As an undergrad, I was told that the former approach is correct only
if you have a model for the dynamics (e.g. Ohm law and you perform a
least-square fitting), but not if you deal with a distribution and you
pick random draws from it (in that case, one should maximize the
probability of drawing the data which were actually observed and this
leads to likelihood functions).
The two approaches do not seem equivalent to me, but I cannot believe
that this distinction is ignored in practice...
Many thanks

Lorenzo