I'm interested in estimating the distributions of a few skewed datasets, for example extreme heat, and extreme rainfall.
There are many distributions that can be fit to these kinds of data, for instance, this page shows an attempt to fit multiple distributions to flood data, including Generalised Extreme Value, Generalised Pareto, Wakeby, Lognormal, and Gumbel distributions.
The fits look like this:
The page decides to use the Generalised Pareto distribution, based purely on statistical performance. There are a few problems with this that I can see: First, I can't see the underlying data, so it's possible they are fitting on only a small handful of data, and also possible that the coarseness of the histogram is hiding interesting features of the data (e.g. a down-turn near zero). They don't provide uncertainty estimates on the performance stats either, so it's not clear if the other distributions' confidence intervals overlap. It's also possible that the sample they're fitting is biased somehow, and so skewing the result towards the a particular distribution.
With the data that I'm fitting, I'm seeing quite similar results between Generalised Extreme Value and Log Normal - at some locations, the GEV fit looks better, at others, the Log Normal fit appears to do better. However, they are all always the same kind of data, and so I feel like I should always use a consistent model. As such, I would like to know:
Is there ever a purely theoretical/conceptual basis for choosing one distribution over another, assuming that the distributions perform similarly?