We propose a new three-step model-selection framework for size distributions
in empirical data. It generalizes a recent frequentist plausibility-of-t analysis
(Step 1) and combines it with a relative ranking based on the Bayesian Akaike
Information Criterion (Step 2). We enhance these statistical criteria with the
additional criterion of microfoundation (Step 3) which is to select the size
distribution that comes with a dynamic micro model of size dynamics. A
numerical performance test of Step 1 shows that our generalization is able
to correctly rule out the distribution hypotheses unjustied by the data at
hand. We then illustrate our approach, and demonstrate its usefulness, with a
sample of commercial cattle farms in Namibia. In conclusion, the framework
proposed here has the potential to reconcile the ongoing debate about size
distribution models in empirical data, the two most prominent of which are
the Pareto and the lognormal distribution.