I have a dataset with two variables: X and Y. X is a treatment, and Y is a response. I want to model Y = X using a general additive model where I then choose one distribution from about 8 choices. I was going to use AIC to select the model. However, a couple of statisticians suggested that this was inappropriate. I am not sure if I am missing something or asked the question poorly.

Y is continuous, so my choices of model are the following: Normal, Gamma, Inverse-Gamma, LogNormal, Weibull, Exponential, Pareto2, zero adjusted inverse Gaussian, and several others.

I have no prior experience with the data. There is no literature to draw from to better understand these data. As far as I know there is no theoretical basis to think that the Weibull distribution will give a better fit than the Exponential.