Distribution comparison by AIC I'd like to compare several distributions fitted to one dataset (of i.i.d. random variables) by AIC. Do there exist some specific rules of thumb for such a situation?
It seems that most of such rules are either for regression models or some extra conditions are needed (e.g. models are nested and sample sizes are large, as in book by Burnham and Anderson).
To be precise, I have a distribution $F$ and a distribution $G$, the sample size $n=100$,
$$ 
AIC(G) - AIC(F) = 17.9.   
$$
Can I claim that there is substantial evidence that the fit of $F$ is better than that one of $G$?

AIC penalizes the likelihood by the number of parameters of the model under the assumption that a less complex model is preferable. The rules of thumb you mentioned are not specific to regression models, you can use them here as well, though they are only rules of thumb, so there are no guarantees they would be meaningful.
When comparing the distributions, the number of parameters wouldn't usually be your biggest concern. In such a case, you care about comparing the likelihoods. If the models are nested, there are not only rules of thumb, but rigorous criteria for such comparison since the procedure is a likelihood-ratio test where the test statistic follows the $\chi^2$ distribution. In fact, likelihood-ratio tests are common criteria for judging goodness-of-fit in such cases.
